The prolixity I have trouble with is less present when Tatum records with a small and strong group. Here's an example, with Ben Webster (tenor), Red Callender (bass) and Bill Douglas (drums):
The marks of his style are there in his solo-rapidity, ornamentation, pattern-running, but there is more breathing; more space.
But then, after his solo and Webster comes back in at about 6'20", I find it hard to understand why he goes into runaway train mode behind the soloist. It's not as if he's playing tasty counter-lines. It's as if he simply won't stop soloing.
I guess if you want to really focus the discussion, you can look at one of Tatum's most archetypical solo performances-Elegy:
Here's my take: Once again, it's dazzling in many respects, but I find it the kind of over-amped, hyperbolically emotional playing that you could expect to hear accompanying a silent movie. He is not, however, following a visual analogue for utilitarian purposes, so his shifts in style seem contrived and show-offy. The jaw drops at the technique, but the heart-at least mine-stays closed.
I actually think that Tatum's rhythmic variety is the most interesting part of his music. Even though there are certain "set-ups" that signal what's coming up, there are also some fabulous shifts in time and in conception. Naturally, this is easier to do in a solo context and I think this version of Tea For Two is a great illustration of what I mean:
If I played piano and not trumpet, I'm sure I'd have to come to terms with Tatum in one way or another, as you would with Bud, Monk and your other venerable elders. I might be cowed by his technique, but I might also say: if I had what he had, I might be able to do something that reached even deeper into the heart of the listener.