Midi is a hardware and software specification. It is not very fast by modern standards and even back in the day it wasn't considered that fast. It works fine with with one device on one cable controlling another but when multiple devices on different channels are controlled by one port, the timing gets muddy to the point that timing errors are easily perceived by the human ear. That is why there were multiport adapters for all the big sequencing platforms for the ST, Mac, Amiga and PC. Each synth in a complicated setup could have its own Midi port.
On the hardware level, Midi is a serial port with an opto isolator and a fixed data rate to be exact. The serial to Midi adapters added the opto isolator to the Amiga serial port. The Midi specification has input and output and thru ports and most devices have at least input and output ports.
The ST had Midi interupt service routines in ROM for the MIDI ports which were pretty fast and a programer could substitute these for custom routines by simply switching an interupt vector. There were MIDI functions in the ST's bios as well. This was the foundation upon which all ST midi software was built.
The Mono Monitor was indeed a plus and made doing complicated sequencing easier on the ST but I think it was a combination of factors that gave the ST the lead in Midi. It was simply having the right hardware and software at the right price at the right time. For the Amiga, the same thing happened with the Video Toaster and even before that with earlier video and animation software and hardware that led to the Toaster.