This API is actually a bit horrifying from a security perspective. In addition to allowing you to use MIDI keyboards as input devices on websites, it also allows websites to send binary firmware updates to MIDI devices. The reason is that it's common to use custom firmware to backup/restore settings and enable neat effects and functionality on MIDI devices.
Mozilla's engineers have reasonably pointed out that an attacker utilizing Web MIDI could use MIDI devices as a stepping stone to launch an attack against the user's PC outside of the web sandbox. One such attack might be by reprogramming the device to appear as a standard USB computer keyboard and "typing" commands to the host.
At least one well known manufacturer has vouched for the technical safety of their musical instruments, noting that they're physically designed in such a way that the MIDI firmware can't alter USB firmware. But there's no way to know that every MIDI device has been similarly well designed.
As neat as Web MIDI is, I think Mozilla and Apple probably made the right security call here.