Futsal, a close relative of association football (i.e. saaaarker) essentially does this already: there are other subtle things being kept track of (which might've helped this past weekend as "foul" counting could be another duty taken out of the centre referee's hands?), but timing of the game is in the hands of an external official at the side of the game.

Weirdly, I've had (and seasonally renewed) the correct patch to referee futsal games for several years, but have yet to use it in anger as they're mostly youth level games and I far prefer adult indoor games where I can deliver sarcastic comments as part of the process.

Moderators, eh?