...but I also can't think of any reason why drummers would not learn piano (or some equivalent).
You're right, I think we're in agreement on this.
I'm just pulling this part of your quote to play devil's advocate with. My response would be that some drummers won't learn piano or any other instrument simply because they don't feel like it.
I don't mean that to sound flippant; it's exactly how I felt during my first decade of drumming. I could appreciate good guitar, keyboard, & bass players, but I felt absolutely no need, and had no interest, in exploring their instruments. The first part of my epiphany came after meeting a group of guys who liked to jam together all the time - and they honestly didn't care what instruments they were playing. It's not that any of them were necessarily good, per se, but that they simply didn't have a notion of "I'm the guitar player," or "I'm the drummer," or whatever.
The second part of my epiphany was after playing in a band with a guitar player and a bass player, who weren't bad players, but who just couldn't seem to compose a song and it was really holding us back (it broke us up, as it turned out). It seemed very simple to me: find a cool riff, match it with one or two other cool riffs, have an interesting melody (or hook) ride over the top of it, arrange it in a nice way and call it good.
I thought, "Hell, even I could do that." And besides, these other cats I know don't limit themselves to any particular instrument, so why should I? So I bought a 4-track, a drum machine, a guitar, and a bass and started figuring out how to play (with much help and guidance from a non-drumming guitar player friend) and I was right: composing wasn't all
that hard. I won't claim to be any sort of genius at it, and my playing skills with strings are still rudimentary, but I was able to get a lot of material committed to tape and I eventually put drums to a good chunk of it, and yeah, it informed my drumming quite a bit. I could have stuck with it and got a lot better at it (as with anything else) but mostly I just like playing drums.
So it's easy to imagine that if I hadn't wasted a lot of time with players who could play, but couldn't write; and if I hadn't been exposed to some hacks that didn't care if they played drums or guitar, that I might still be in my earlier mindset where I thought drums were for me and notes were for everyone else.