I think there’s a divide here in the narrative of rape. Classically, rape is a crime of a random scary person, because those cases are the most visible. I think the random rapist walking the streets for victims indeed is a power trip.
Date rape we know (at least I know) is far more pervasive. Or worse yet pedophilia. Both of these things are far more common than reported because the victims don’t come forward. Sample size and all that, but I’d say based on my experiences that random rapists are the exception and not the rule.
It is likely, if ever these other categories of sexual assault get proper scrutiny, that other motivations come to the fore. But my guess is non-random rapists (i.e. the bulk) are motivated by getting their rocks off in their preferred way with little risk of punishment.
I say this because I’ve known a lot of victims personally. Some I found out anecdotally, but still none fall into the category of random attackers. And I would categorize most of them as sexual opportunists. Of course, I don’t have all the gory details, but most don’t exhibit an aspect of power from what I know.