I've seen some really great early music (1200s?) MIDIs put together by doctorates, and to simulate the early instruments, each note is hand tuned (or perhaps re-tuned using software, I'm not sure). Those instruments were not diatonic.
Additionally how could you express a solid sweep from C1 to C8? Not that you could or want to, it is just that it isn't something MIDI can handle.
There are a lot of compromises and hacks and such. Recently at PyOhio I saw a presentation about the raw data of the Open Goldberg Variations, and some of the raw data from that device has pressure sensitivity readings outside of the scale of MIDI.
Most artists I see wind up using OSC. It is lower level and more general purpose, and you can convert to MIDI (lossy) if you need it. I was thinking of how to sum this up, but I guess MIDI is good for what it is good for, and like most things, aren't much help when you go down a deep rabbit hole. I love MIDI though!