Perhaps this is part of what is coloring my opinion: as a semi-professional musician who occasionally plays with serious folks and who knows a lot of both DMAs

Perhaps this is part of what is coloring my opinion: as a semi-professional musician who occasionally plays with serious folks and who knows a lot of both DMAs and "self-trained" successful pro musicians, I don't know if there is a lot of value in music school once you learn how to practice an instrument (a difficult task in itself). As a a substitute for doing the legwork of getting gigs and sitting though a ton of shitty ones, a collegiate musical education might serve well. But beyond that networking, it's just time spent learning scales, tunes, technique, and so on. Go to summer camps and play with as many people as possible, and you have a much more useful experience, IME, especially for the price. That's my observation, not the only solid opinion on the matter... but it is my opinion. For what little it's worth, I've been taking online classes in math with an eye to learning calculus and staistics... I feel like that skill alongside my current programming skills will set me up to do some really interesting stuff in 24 months or so. Really, I feel like I make plenty of gains in understanding just by doing a ton of exercises... I wouldn't have been able to do this when I was 20, but I'm a lot more disciplined as a 40-year-old... so maybe that is my point here: as I've gotten older, my experience is that the kinds of self-directed learning which might be the core of what a PhD program is instilling in people, are a lot easier to practice. But of course, that's my own possibly idiosyncratic understanding of a PhD and learning. I don't know if other folks would agree. In any case, consider doing 20 minutes of math every day for a while and see if you like it... it's kind of fun. It won't rock your existence probably, but if you do it long enough you'll get better at it. Maybe it would be easier in the context of an undergrad class. Maybe you'd be better of with an actual teacher grading your work. But you are likely capable of doing that work on your own.