Where it makes the biggest difference for me is audio editing. But if I can be more accurate with MIDI too, why not? It makes the capturing of performances more accurate.
The PGMusic statement "This is about 4 millisecond resolution" tells me they are also using 120 for the Tempo to determine this. Like I said above, at 120 tempo and resolution it's 4.17 milliseconds. Glad to see them verify my results!

If you play a grace note quick enough and at the right moment in time it can cause the two MIDI events to be written to the same time slice. I've had this happen, which is what started me along the MIDI resolution path.
I guess one other example could be a drum roll or flam on an electronic drum set. Recorded at 3840 would be much more real than 120 ..

I do not work here, but the benefits are still awesome
Make your sound your own!