solid subjects like math and coding are full of easy problems.

You are straying far afield from colloquial usage of the term "easy" - yes, solid subjects like math have solid problems: objectively verified if they have been solved or not. Yet, with 8 billion people on this planet and mathematical prizes ranging up to $1M and more, many of these problems you are calling "easy" have gone unsolved for decades - and a few of those are starting to be shown objectively solved via use of the new LLM tools...

Squishy subjects like music and sociology are full of hard problems

Again with the colloquial usage - squishy is a better term than "hard" - you can present very heavily referenced and logical and self consistent positions in subjects like sociology, psychology, literature etc. and "the powers that be" may simply refute your position as incorrect or irrelevant without presenting any concrete evidence or argument as to why other than "it does not conform to our (undefined, unexplained) standards of practice."

On the other hand, a "darling of the field" may present a position and be instantly loved and accepted by the field, again for undefined and unexplained reasons - though rather transparently the true reasons often appear to be pedigree, likeability, stroking of the establishment's egos and pride... LLMs can be trained to do all those things, but the fact that they present in an LLM body will just as assuredly damn their viewpoint as if a black woman walked into a Southern University with a revolutionary new idea in the 1950s.

LLMs which, by definition, can only produce output that is within the distribution of their training set.

I'm fairly certain that's not a strict definition - LLMs also seem very heavily influencable via their context window inputs, though those are more limited and transient than the training set.

there is no way an LLM finds it and recognizes it for what it is.

Again, I believe if you study large populations of music listeners, tease out what drives their opinions, distill that, and feed it back into a LLM-like composition engine, the LLM approach may be able to produce both unique and paletable productions. Now, you may need a fleshy front-man/woman to appear to perform the composition, because that is part of the formula - relatability, the audience often likes to fantasize about being the performer(s) and that's not going to happen for a data-center.

For comparison, a LOT of popular songs/music has been written by old Jewish men - but they don't perform their compositions because they're not personally appealing to the target audiences...

You can’t achieve that if a machine speedruns all the little tasks for you.

I agree, for a speedrun of a bunch of very common material. I knew a young singer, attractive, good voice, had a good backing band - she went fairly far in "America's got talent" but was knocked out in the last round before TV appearance by an apples/orange comparison - only one was going forward and the two weren't really directly comparable, her band lost. Never made sense to me until a few years later I went to Disney's Pleasure Island - they had an array of talented bands performing and as I walked from one to the next through the night, I saw one after another after another young female singers who were all just as attractive, talented, backed by just as good of a band... she was a commodity - as talented as you could ask, more talented than many national acts, but not unique.