For the same reason that sporting organizations regulate the equipment allowed during play - the make sure the playing field is reasonably level.
>For example people used to talk about APM in SC2 as a sort of measure of how good someone is. Why should that be?
Because dexterity has historically been a basis for comparison in recreational competition.
>It's a strategy game.
It's a real-time strategy game, which is an important distinction. Chess is a strategy game, and by its design guarantees each player an equal number of moves. SC2 is a real-time strategy game which makes no such guarantees, and if you have the dexterity to execute your strategy faster than your opponent can respond to, you should be rewarded for that.
>Imagine if you could express your ideas effectively into actual game actions?
Imagine the cost of such an interface in today's society, especially compared to a regular USB keyboard and mouse. Now imagine you're a game designer. Do you want to build a system that explicitly favors those rich enough to purchase the best equipment, or do you want to spread your playerbase as widely as possible?
Perhaps in another few decades, we can start rewarding the people with the "best" brains, but as long as we exist in meatspace, people are going to want to test their meat-skills against each other.