But then you have to give up one of your attacks to move or do anything else that takes an action

Yes. That’s generally how it is. If you first have to run to your opponent to hit them, you can’t hit them as often as if you were already there.
If you shoot while moving, you will have a lower effective rate of fire.
But my actual point is: turn-based combat is always an abstraction. I like to abstract it a bit more than DnD does, simply to avoid wasting any game time on arguing about action types.