What problems wouldn't it solve?
Assuming (correctly) that kids can engage in philosophical activity and that it leads to scientifically-proven benefits (above and beyond the intrinsic goodness of philosophical activity itself as would be attested to by the greatest philosophers), it only stands to reason that adults can engage in it as well. Assume that we can all get on the same page about this and that within, say, a generation, we'll have a philosophically-educated populace (perhaps worldwide). What might that look like?
In Prologue to an Aristotelian End of History, I outline what I take to be the norms, or the form if you will, of a society that has taken up the 'Aristotelian project' to its ultimate expression. (The basic norm of Aristotelianism is something like intellectual perfectionism, and does it get better than perfectionism? How do you improve upon it without incorporating it as a norm? We've reached a normative limit here, I think, and an irrefutable one at that.) I can only speculate on what the outcomes, the matter or content if you will, of such a social order. And at this stage of things I am not sure how exactly to separate issues of said form and said content. For example:
Does this represent talk of form or of content: Philosophy for Everyone (hereafter P4E) would go a very long way toward addressing the aims and concerns of all the major ethical theories. It would satisfy the requirements of consequentialism; see the link above about scientifically-proven benefits for kids. It would satisfy the requirements of deontological theories insofar as those are focused on what it is to treat humans with the utmost respect for their rationality and cognitive freedom. And it certainly satisfies the requirements of virtue ethics insofar as the very activity of philosophy leads to cultivation of good character.
Consequentialists, deontologists, and virtue ethicists may be in disagreement on matters of justification (and Hurka treats perfectionism as a consequentialist theory, but, well, are virtue-ethicists qua intellectual perfectionists also consequentalists in some sense, given the desirability of intellectual perfection qua human telos?), but they can all agree, overlapping-consensus-like, on a prescription for P4E. Then we get everybody on board with a justificatory project which applies standard philosophical methods such as dialectic to identify any and all grains of truth in each of the major schools of ethics.
Then, we get everyone (well, everyone who is minimally interested and there will still be intellectual divisions of labor, etc.) to fully and adequately assess the very principle of intellectual perfectionism as expressing the best of what philosophical inquiry leads us to. In other words, we end up assessing theories as Aristotelian reasoners (whatever else we arrive at as expressing ultimate philosophic inquiry). That is a formal principle of an ultimate social order, but where does that get us, outcomes-wise? That's where I can only speculate. But the very adopting of the formal principle is an outcome of sorts - it'll be a real-world application of some philosophical reasoning, instantiated across a population or populations.
Now, in principle, all this can happen within a generation with the proper information-transmission mechanisms, and I have good reason to believe that this can be done despite all the obstacles thrown up by social media. Whatever else, philosophers as a community need to get on board with the project (and they're being drowned out in the discourse by whatever crap goes viral on social media). But you really don't mess with philosophers, much less with a community of them; if they (in consensus no less) endorse X, they'll have really good reasons for doing so, and beat out objections to X, and soon enough X will be a social norm.
We also have to consider that within a generation from now, AI technology will be a generation more advanced. AI works on the principle of what's called 'machine learning,' and among humans Aristotle has been a premiere instance of (rigorously systematic) human learning. What there is to learn will probably see a convergence between the best of human learning and whatever AI learns. This includes moral truths, and we already see something about what moral consensus can emerge even among disparate schools of ethics -- i.e., that intellectual-perfectionist learning across a population or populations of people is a grand idea, arguments against which would by necessity be self-undermining. (What better argument can you come up with, ethics-wise, than perfectionistic learning being morally obligatory?) Now, our best ethical reasoning and/or most compelling moral truths, indicate that there are goods for conscious agents, and whether or not AI ever becomes conscious, it will recognize goods for us humans qua conscious agents that could not be overriden by what AI learns in addition to that. It's analogous to the best moral reasoning we humans have for how we ought to treat the other animals. (Compare/contrast the state-of-the-art moral reasoning on the ethics of the treatment of animals with current mainstream practice in which, e.g., inhumane factory farming carries on with impunity. Obviously there's a disconnect. Assume that there would be no disconnect between ethical truth and how AI would consider the moral status of humans.)
We should also distinguish "philosophically-educated populace" from "populace of full-time philosophers." There is still intellectual division of labor. But the love of wisdom as an organizing principle of life for all members of a populace can be instilled from a young age and expressed in whatever activities that are suited to each person. Living thoughtfully and intelligently is the common or generic form of human flourishing or eudaimonia or self-actualizing; the content will be expressed on an individualized basis with diverse and complementary excellences.
The form of a philosophically-educated populace would be such that everyone (or near everyone) could blog at the level of this here blog if they so desire. But the content of what they might blog would be anyone's guess. If everyone is blogging (or able to blog) at this level, what builds - presumably exponentially - from that? They're not going to be blogging all day long about the latest celebrity gossip or stupid politician (since politicians wouldn't be stupid any longer), will they? Perhaps once the basic problems of stupidity in politics are solved, and a strong overlapping consensus in ethics is reached (intellectual perfectionism seems to fit the bill pretty well for that), and virtue epistemology is the norm (intellectual perfectionism again), are we left to discuss metaphysics and the arts, which would likely converge on the 'fundamental' topic of philosophy, the meaning of life? I mean, what else are humans going to do with all their time when AI is overseeing the process of material production with all the inexpensive and abundant products being generated (although 'living small' and simply may be the norm of Aristotelian society; I mean, how many SUVs for the sake of getting to nature and family gatherings [first and foremost] would there need to be, assuming a zipcar model is adopted, and how would humans not figure out the optimal arrangements here without input from AI-computed logistics?).
As for politics: I'm not a leftist, i.e., someone hostile to capitalism or to the wisdom of Western tradition. Would a philosophically-educated populace be leftist? The PhilPapers Surveys of philosophers suggest that a plurality of philosophers are egalitarians in politics (given an exhaustive three-way division between positions generically labeled "egalitarian," "libertarian," and "communitarian"). But it's my belief that leftism exists as a program for addressing human problems that P4E would solve anyway. I don't know what exactly would be left for the political sphere if everyone is on philosophy and achieving abundant goods of life as a consequence; politics is about fighting over what would be crumbs in contrast to what would be achieved with P4E. The thing with leftists as they are today - short of their being intellectually enhanced by P4E - is that despite their pretending to possess a superior intellectual and moral compass, they somehow have not figured out that P4E would solve the problems they want to solve. (Is it really inequality per se that's a problem, or not enough people achieving their potentials that's the problem? Gee, that's a no-brainer. Also what should be a no-brainer is a libertarian principle recognizing intellectual-and-hence-practical freedom as a formal condition of properly human living, along with a capitalistic, private-property principle based on the recognition that material value-production originates in the individual, private intellect.)
So I'm not really concerned about P4E turning a plurality of people into leftists. Besides, getting really superior at dialectic involves doing what leftists don't do, and that is addressing the strongest version (as per Dennett/Rapoport Rules) of an opposing position, and in the case of capitalism that would entail having to take on Rand and Mises and Nozick and the 'Dougs' and Sciabarra and other giants of pro-capitalist thought in full good faith. (And it's a two-way street there, but something tells me the libertarians/capitalists, especially the neo-Aristotelian ones such as Rand, the Dougs, and Sciabarra, are ahead of the leftists, who don't seem to talk much about Aristotelian themes.) And once you take on Rand/Dougs/Sciabarra in full good faith you end up taking on Aristotle in full good faith and we're right back to P4E again (or is it A4E, Aristotelianism for Everyone?). (And/or IP4E, Intellectual Perfectionism For Everyone?) There's nothing to be concerned about in regard to where people doing philosophy properly will take them substantive-beliefs-wise. (Also, bullshit political and networking dynamics in academia can't get in the way of P4E/A4E/IP4E fully applied; there can't be the currently-prevailing "liberal" hubris that involves seriously underestimating (capitalist) libertarianism in its strongest, i.e., Aristotelian-intellectualist, formulations.)
A4E would mean doing dialectic in the spirit of Aristotle, and at that level of intellectual productivity we would then have the proper platform upon which to do what is an ultimate dialectical showdown in the making, Aristotle vs. Kant, since we just don't have enough brainpower on this topic yet to figure out how that might go down if these two titans were brought back to life. (Aristotle vs. Kant, mediated by Hegel? Presumably Aristotle already presupposes/incorporates Plato.) I don't know enough about Kant to say yet, but would A4E realize his ideal of a Kingdom of Ends? Does it realize Hegel's conception of an end of history? Does it realize Nietzsche's rather nebulous references to Ubermensch?
And let's not make the silly mistake of assuming that intellectual perfectionism means exclusive focus on perfection of the intellect to the detriment of the other facets of human nature such as emotion (in which we also exceed the other animals in complexity and sophistication); indeed, it is through intellectual perfectionism that we can optimally learn what best actualizes our human potentialities in all facets of life. This includes perfectionism in the area of nutrition and physical fitness science, in which case fitness geniuses such as Cole Robinson and Paul Chek will need to enter into the mainstream cultural dialectic. (And dialectic has something to do, may even be synonymous, with intellectual perfectionism, something about all-embracing learning and culling-together.... Have, e.g, Paul Check and Ken Wilber been 'dialecticized/synthesized' with one another yet? And who all should be 'dialecticizing' with whom? A lot of folks; use your imagination. Cole Robinson knows about Victor Frankl, but does he know about Aristotle? Many gaps to close here, many strands to tie together.)
Speaking of strands to tie together, along with a strict drug regimen to keep one's mind limber, would philosophical activity with P4E or A4E be further stimulated by cannabis used in (Aristotelian) moderation? I'll take that topic up plenty soon in a blog post preparation for which will involve cannabinization, and which will treat of all the subject matter above as already-established presupposition or background (all as a unit, as it were). It should be pretty great.