MIDI was designed around the piano, which is a very low-dimensional instrument. Due to how it works (hammers that hit the string with a given physical velocity)

MIDI was designed around the piano, which is a very low-dimensional instrument. Due to how it works (hammers that hit the string with a given physical velocity), the only things that affect how a note sounds are: when you play it, what key you play, how hard you hit it, and the exact position of the damper pedal (and other pedals if used)%. Pianos have a mechanical system that abstracts your playing and confines it to these dimensions. These are the exact dimensions that MIDI covers. And this is why these days we have extremely accurate piano samples as well as physical modeling synths that sound amazing with MIDI input. However, on other instruments, you have a much more direct relationship with the sound. With a violin or guitar, you physically touch the strings - directly or with some device. That already means you have something like 6 degrees of freedom in physical space, not counting fretting. Plus if you use a finger directly, your playing won't sound the same as someone else's with different fingers. The whole action of playing a note is a complex process in time, not a single event, so you can't capture it as one set of parameters. Then there's things like tapping on the body of the instrument, not the strings. You'd basically need a model of the contact surface that touches the string, its physical parameters, and its precise motion in time at high resolution, to accurately capture all possible playing techniques that people actually use. What we've done with sheet music is standardize many of these techniques into instructions that players can perform. It's obviously only a much lower information version, but it's there. Of course, if your question is "can we encode everything in sheet music with MIDI" the answer is obviously yes, but it's not standardized. A given virtual instrument could hypothetically implement anything you could write a score for (perhaps with an obscene number of samples or a really clever modeling synths) and be controlled by MIDI, but only a tiny subset of these options have vaguely standardized mappings to MIDI. MIDI is a very limited standard with tons of room for expansion, and only the most basic MIDI features interoperate between manufacturers. You can make MIDI music sound amazing with specific setups (and this is effectively how a lot of modern music is produced), but you can't make General MIDI music (the standardized subset) sound amazing. The other issue is that sheet music is at a higher abstraction level than MIDI. It leaves more to the interpretation of the performer, but it's designed to be easily interpertable. For the portions of this that MIDI does express at a lower level, it's very hard to infer the higher level representation. % This is excluding prepared pianos and techniques like reaching in and touching the strings, which are rare; of course technically you can do crazy things to a piano, but in practice we don't.