I always viewed the overhead view as a substitute for the other senses. If you are walking about, you look all around you and you hear what is happening. You also have a sixth-sense as to what is approaching from behind you. This is actually a trait more accurate to reality than the FPS view can describe. In an FPS, you walk to direction you are looking, which is not a good model of reality. You can look around as you are walking using short-term memory and instinct to know where to step.
I think a FPS is a strategy game as well. How much ammo can I spare? How quickly can I traverse this open area? What are the chances of there being more guards? How can I lure them away? Strategy can be applied to almost any game, it really depends of the focus or main elements of the game that gives it its genre classification.
