Maybe it also requires a certain amount of "saving up," and if you use it, you have to rest a bit before using it again.

That's always been my personal reading of the Killing Curse. And also, I feel, where the Death Eaters seeming unwillingness to deal in all things Muggle proves to be their disadvantage. Yes, AK takes a lot of magical power, but how easy would a Petrificus Totalus, followed by a nice slit to the throat be? Possibly, the DEs feel this is inelegant.