Keep in mind the keepers are expending much less engergy

by Captain Robb, Monday, June 27, 2016, 11:09 (2852 days ago) @ oviedoirish

A game that's still tied after 120 minutes might not ever end - the keepers are still (relatively) fresh while the field players would just be weakly lobbing shots from 30 yards out.

Maybe every OT period you get 1 more sub? They wouldn't carry over from period to period so you don't get to save them up, but just one fresh pair of legs every 15 minutes in OT. And after 120 minutes a player that was subbed out in the first 90 can come back on. Keepers can't be subbed out unless they get a card.

Of course, then you run into the problem that the MLB All Star Game has, where end-of-the-bench players are deciding an incredibly important game (and in the ASG, those late inning subs are coming from teams who have no earthly chance of playing in the postseason... but that's just one of a thousand things wrong with MLB's entire setup).