MIDI is not inherently lossy. You could encode anything in it, just as you can encode any novel as an integer.

In practice, though, transformations from audio to MIDI discard an enormous amount of important information, with the possible exception of transcriptions of performances on piano (where volume, frequency, duration and a good physical model of a piano are enough to reconstruct everything important about the signal) and similar instruments.

No, it's lossy. It's an event model at a fixed data rate. You can only do so many things sequentially, even if you could represent any possible musical concept as a MIDI event. So even if you're not sticking to note-on, note-off, it's still extremely lossy.

MIDI is an extraordinarily lossy music representation. Even Claude Shannon would facepalm at the assertion that it could, in theory, represent audio faithfully. It is not its purpose, it is decidedly not its practice, and it is a ludicrously irrelevant example of pedantry to say otherwise. The false equivalency asserted by the commons can be aggravating :D