I think the main original purpose of MIDI was specifically for live performances.
So if you had a drum-machine and several synths one player could operate any of those with the same keyboard or even at the same time.
This was in the 70's I think that it began so the computer aspect wasn't even part of it yet. On the computer I will use it to play virtual instruments.
Oh also, you can make .midi files that are portable music for any instrument.

I've never seen one of those Yamaha drum mic devices before, but that's pretty cool.