In these days when STEM is so promoted, I think sometimes there is too much tendency to dismiss the arts and humanities as complete lightweight fluff compared to STEM. Perhaps there are some subjects which fall in this category. But I know, for instance, with music theory and composition, the heavy stuff can get fairly complicated and technical very fast. Certainly few people would be dismissive of the technical training required to be a virtuoso player.
I think this is the same for other "liberal arts" subjects too. Take linguistics -- from what I know about some of the linguistics concepts that pioneer translation software, speech synthesis, natural language processing, etc., linguistics is hardly "fluff" and requires some years of deep study to be an expert at.
The Economist's monetary chart is solely based on supply vs. demand.
In many subjects, I think extremely gifted autodidacts are pretty rare. No matter whether its the STEM subjects or the arts or anything else, I think most people benefit from an environment where like minded peers can bounce ideas off of each other.
When I look at Wikipedia's list of autodidacts:
https://en.wikipedia.org/wiki/List_of_autodidacts
I know this is just a sample, but at first glance, the list of autodidact scientists and engineers certainly seem to be of comparable size with artists / musicians / etc.
EDIT: I will add that I agree with other above posts, that one of the biggest barriers for the modern autodidact scientist / engineer is that it is really hard to home-tinker with certain concepts. You can program at home very easily. You can make circuits and robotics at home. You can even "group buy" small order electronic bare boards from contract manufacturers with all the difficult-to-hand-solder parts already taken care of.
It is nearly impossible, however, for a home tinkerer to get access to $100K scopes, electron microscopes, GCMS / NMR machines, or any other "big equipment" of this nature that you can think of. Heck, depending on what you are doing, you probably even risk a run in with "the law" these days from tinkering in certain sectors of hobbies like home chemistry or home biology.
To me, that's pretty much the barrier for non-college STEM in a nutshell.