> asking the server "is it legal for me to move to x,y,z?"

These questions are not always straightforward. Why can't you do this in a shooter? Because any mouse position on the screen is valid. How do you know if the user physically moved the mouse or it was some other software that moved the mouse cursor?

How do you know the user genuinely decided to aim at a random enemy, instead of relying on an on-screen display of player information that is not normally available?

You can't do everything on the server side. If you could, it wouldn't be an interactive game.