I think you credit women with entirely too much ~ many men need no stimulation at all.
To some extent that is true. Some men could satisfy a sexual desire regardless of the woman's age or appearance.
Still, if a man is going to force himself on a woman, why not make it an attractive one? Sure, she doesn't HAVE to be attractive, but wouldn't that be what most men prefer?
And again, what about the violence involved in rape? If it was just about sex, all the rapist would need to do is keep the victim from resisting or escaping. Yet in many instances, the victim is severely beaten, even after the sex act has ended. Why is that necessary if the man has already satisfied his sexual urge?
I think there can be many causes for rape, and that there are different kinds of rape. Sometimes, it is just a case of a man unable to control his sexual urges. Sometimes, it is a case of power and control. Many times, it may be some combination of the two. I don't think generalizations really apply.