I mean, I play guitars and pedal steel, banjo, dobro, accordion, etc. all acoustically (or, more likely, "in the analog domain"). Maybe I just need to practice more or listen harder.
Do you have any suggestions on how I can improve my timing and/or hearing to experience this?
Sure if you're sending things to and back through a DAW or whatnot it can get noticeable, but that's processing/software time, not MIDI 1.0.
I can't tell the difference between a 320kbps mp3 and FLAC either, but I'm not worried about it.
Even in highly time-aware percussionists, sensitivity to timing is way below the timing delays that MIDI causes (e.g. with note smearing in a chord).
The next roadblock on the way to truly concurrent chords would probably be controller readout. I know nothing about how those are typically implemented, but I strongly suspect sequential readout.
Changing MIDI to have "defined latency" is a fundamental re-engineering of the entire protocol.