I think you'd need to slow down starcraft for it to be playable as the same game. People hit 60-100 actions per minute, like jumping around the map and directing units, setting build queues. Without hotkeys, you'd drop to around 20apm, and you'd be unable to do any micromanagment of units in battle. So it's not that any one action is impossible, just that lots of tactics that require many actions would be impossible.
Maybe for hardcore sport-like starcraft players this is true. But when I played starcraft I never did nearly anything like 100 apm neither my game ever required me to. Yes, that'd probably mean I'd lose miserably if I ever play 1-on-1 against a hardcore sport players, but that's not why I would be playing it and I'd probably never play with them anyway, I'm not in the same league. So I think for a casual player it would be OK. And hardcore players would have their hardcore setups.
