Of course it's impossible for humans. Humans are used to clicking multiple times to do an action. Some actions you want to take in the game are very important, failure to do them correctly can mean a lost game, for example moving units in combat properly. This means that it's better to spam click that action a few times to make sure that the button press is registered properly, because it is possible for button presses to fail due to hardware, software, and most often a coordination error. This means that essentially every player has a much higher APM than EPM, but it's really EPM that counts. APM itself is mostly irrelevant.

Hmm, seems like it might be interesting to add a slight error rate for AI clicking and see how it handles it?

You only need excess dexterity than your opponent, and only for a couple seconds, to decisively win a match in SC2.

Error rates, EPM and APM are all red herrings.

Right, one example I remember from watching the games back in January was stalker micro. The high EPM of the AI allowed it to micro them picture perfectly and blink every single one away right before it died. In doing so it won a battle against impossible odds, and the announcers even commented on how it was way beyond the capabilities of the best players.

That exact strat is the reason they implemented the APM limit, it was a cheese strat only a machine could implement.