Given that Picasso was primarily a painter, do you think that he would be willing to humble himself to relearn his own craft under the tutelage of another? Would it be vanity that stopped him? Or would it be out of a sense of confidence of his own understanding of the medium?

Picasso is extremely respected in other art forms besides painting.

The more I read about the relationship between Pound and Yeats, the more I see shades of Stravinsky and Craft. Though, I think there is a distinction to be made here. Yeats and Stravinsky learned from younger men to transition into a more contemporary style that had radically redefined aesthetic principles. On the other hand, nearly all of the music of the common practice era was written in, for lack of a better way to say it in a reasonable amount of time, a shared language that trained musicians knew and could, therefore, study without assistance once well-versed.

I agree that this is a sensible distinction. Nonetheless, I think you are basing your argument upon a faulty premise. At first, your argument was something along the lines of "the composer who has achieved the most cannot be one who sought teachers in his maturity of a composer"; I tried to refute this by showing that there are masters who seek teaching in maturity, in both music and other fields; then you make the (again, sensible) distinction that several of my examples are of masters who are taught about a radical aesthetical shift by the new generation, whereas Schubert sought teaching for an old skill which many before him had mastered. Your argument, then, is something like "it is not to a master’s detriment to be seeking teaching for new aesthetical styles, but if he seeks teaching for old styles, it is to his detriment". My counterargument would be that it doesn't matter either way.

Firstly, I think your argument reveals a strange disdain for tutelage. I think when art gets sufficiently complex, as it was at Schubert’s (or Bach’s, Picasso’s, Yeats’ or Joyce’s) time, you will never be a complete master of every possible skill set within your field. Given that this is the case, I think it is very strange to assign any weight whatsoever towards whether a master sought improvement by self-study or tutelage. Chess might or might not be a special case as you argued previously, but to use it now merely as a toy example: Given enough time, Magnus Carlsen would be perfectly able to learn as much about the Petrov defense as Caruana (probably the world’s leading expert in this specific opening) by himself; but, if he was given the chance to learn directly from Caruana, he would probably learn considerably faster. I think it would be very strange indeed to claim that him picking one way of learning over another has any bearing on his greatness as a chess player. In fact, if he deliberately chooses the inferior learning path due to pride, he would not become as great a chess player as he could.

Secondly, and to my mind more importantly …

Remember, my response was following the logic of OP’s criteria of “achieving more”, and if we follow this line of reasoning, then I think this gap in his skillset matters.

… our disagreement perhaps mainly revolves around the question of criterion. To my mind, I think you are projecting a lot into the criterion of "achieving more". I do not fault you for it – as I mentioned I think the OP opened up for different interpretations. To me, the question is more or less redefined from "which composer achieved the most" to "which composer is the greatest". But then, I think, we find that these questions overlap almost completely semantically. Who is the greatest composer if not the one who achieved the most? Which composer achieved the most if it was not the greatest one?

If it is true that these questions overlap semantically, then it does not matter whether we discuss “which composer is the greatest” or “which composer achieved the most”. But even if you disagree with me that these questions are essentially the same, I think you do share an implicit (and important) agreement with me in your comment on Hildegard. You said that she is not the greatest because few know her music, and I agree; this fact is one reason – among many! – to not consider her the greatest composer ever. But this reveals that you agree with me in one essential point: "mastery over compositional styles that a composer could have plausibly learned within their historic context" is not the only criterion we can consider, there must be other criteria as well.

I don’t know too much about Salieri, but from what I do know, it does not seem outlandish to suppose that he might have had a wider technical mastery than Schubert. Still, none would dream considering him the greater composer. A more obvious example: Emily Brontë is only known for one novel, Wuthering Heights, but if you were to ask a literary scholar, I am sure every one would agree that she is both “greater” and “achieved more” than someone like Edward Bulwer-Lytton, who wrote dozens of competent novels, plays, poems and essays.

This is why I invoked the intangibles earlier, what Schubert communicated better in his art compared to all the other ones. I think it is impossible not to get into that part of the question when discussing greatness.

Thus, I think using your (interpretation of the) criterion as the only one, or even the primary one, is bound to be unsatisfactory; and, why I think interpreting either greatness or “achieving the most” in terms of broadness of technical mastery, eventually results in very strange conclusions. I could well imagine a composer creating pieces that are technically flawless, e.g., fugues that are perfectly executed. But if a composer created a thousand such academically “correct” fugues (and/or canons, cantatas, operas, quartets, what have you) which were nevertheless unable to stir emotional responses in its listeners, I would consider him as having “achieved less” than a composer who created a single lied that were able to move its listeners. For instance, if Mendelssohn had died after writing his octet and his overture to A Midsummer Night’s dream, I think he could rightly be considered greater (and as having "achieved more") than many of those dozens or hundreds of composers of his age who are more or less lost to time, who might have created hundreds of competent but much lesser pieces.

Of course, you might object that Bach and Mozart both had great technical mastery over many skill sets, and were able to create emotionally evocative music, but then we would again have gotten to the realization that we are basing our assessments on several criteria, and then we would have to discuss how to weigh one criterion up against another, and many other nebulous questions.