But they don't; even moderately competitive players can beat the best bots.

That's because the programmers are bad at AI for that kind of game. It just means human beings don't understand how to make a good AI for a game like starcraft. AKA the human being being the idiot that doesn't understand how to make one.

This isn't true, in general a bigger army will beat a smaller army every time.

After you can make equal size armies, the next problem is army positioning and when to take engagements.

Finally, after you can do all that, then you can get an extra bonus to your power by microing really well. But not every micro is about speed - most of the time it's about knowing what to do.

And even at the most extreme, it's less about clicking quickly and more about clicking precisely.