Why would the system monitor all the above and not the gear position. Even a 737-300 will scream Gear to you with flaps out at a certain hight

Matt
Remember this is a military aircraft designed to fly low and slow if it needed to. You really would not want the plane always screaming "Check GEAR! Check Gear!" every time you had to do low level passes, or sneak into a LZ at night while fling below 1000ft..(which is how they train almost every other day), I think that is why the gear handle just glows red when you are that point, to remind the Co Pilot "that if you decide to land, you may want this down for best results" C-130 also train like this too.
And also since McDonald Douglass Original made the C-17, there is no telling what there engineers were thinking, before the "merger" with Boeing.