Having only 16 MIDI channels means that channel identification only requires 4 bits and therefore could be included in the status byte. The most frequent MIDI messages (note on, note off, CC) comprise a Status byte followed by two data bytes.
MIDI transmits 10 bits per byte at 31.25 Kbits per second so a note on message takes 1 ms.
More MIDI channels would have required an extra byte of data per message (unless the number of types of MIDI message was reduced from the existing 8), which would have an adverse effect on MIDI jitter and latency.
They could have chosen to have any number of MIDI channels, not just 16, but I suspect they were mindful of latency and jitter.