Initially, I thought it began with Left 4 Dead, but the PS1 and SNES both allowed for a simultaneous four players with the installation of their respective Multitaps.
Is it because four is the cleanest split you can achieve on one monitor without going all crazy? But some newer online-only titles still issue a hard cap on four players.
Maybe it's a binary thing.

I think 4 players is just kind of the sweet spot for co-op. Any more and it might feel too easy.

It's about console split screen from the old days of TVs. a 4:3 TV splits pretty well into 4 quadrants. The N64 added 4 controller ports and since then 4 has been the default. It also happens that 4 is a good number of people to gather together for a game session whether online or off, and a reasonable number of people to coordinate. There are games with 3 player co-op (like Trine) and it's not a binary thing, just a custom.