I mean, you could, but that would get really gross when implementing certain scales that are nowhere similar to the MIDI tuning (like working out the fractions for a 13-note scale)
This doesn't need to be a trivially human-readable format, but I think maybe it would be nice to allow for multiple pitch representations: floating point frequency, floating point fractions of a semitone in any arbitrary EDO, fractional frequency as used in just intonation, etc..
You could also allow for annotations, like maybe a note pitch is represented as "63.86" in 12-EDO, but it's not just some weird in-between note, it's actually the E that's 5/4 above C, so the file could have an annotation that says that's what the note actually means in this context.
I've heard the recent midi 2 can get around this but it's still a pain with the 40 years of midi equipment that surrounds us.
One way that works for multitimbral synth (which a lot of 90's romplers are) is to only play one note at a time on each channel, and use multiple channels for polyphony. This allows you to individually control the pitch of every note.
The one-note-per-channel trick works okay, but it's kind of awkward. If you want to use all 16 channels, it means setting every channel to the exact same patch, which is tedious. Also, you have to know what the pitch bend range of the synth is if you want to bend by the exact right amount. So, eventually MPE was adopted as an official MIDI standard to provide an easier, more user-friendly and standardized way to do one-note-per-channel MIDI.
MIDI 2.0 has added per-note pitch bend. For anyone making microtonal instruments right now, though, I'd say MPE is probably the best/easiest option.