I have equally muddled thoughts, and I'm supposed to be sleeping, so obviously, I'm going to try and outline them.
Firstly, 'rape is about power' has to be a generalisation because there are too many circumstances in which rape occurs to have one model. But I think you can put power in most models somewhere.
Women and children are more vulnerable to rape because they are physically weaker. The power differential makes it possible.
Stranger rape is rare. It's a sexual deviance. It may be about sexual gratification for some (not all), but they're getting off in a particular situation - where they have all the power. Street girls just aren't expensive enough, nor stranger rapes common enough, for it to be plausible that it is just about getting sex.
Rape by family members, friends, partners ... now you get into very complex territory.
It can be purely about sexual gratification. Non-withdrawal is one obvious example. I raped a man in this way: coitus interruptus, me on top, simultaneous orgasm, I was weak. It was rape - I just didn't realise it at the time. I think this is likely to be the case for most non-withdrawals. Lack of self-control and/or confuddlement about the situation. Worth noting that the only reason I could rape him was that he was powerless to stop me. Had he been on top, I'd have had no such opportunity.
Partners and dates? Twenty years ago. men had the right to rape their wives. 1991 the law changed. That's serious power. And three whole living generations of men who had that right. Some may be rather bitter about giving it up, and if they have wives who are used to it, they can and will abuse that power. I've had some deeply unpleasant exchanges with some of these older men. Extreme culture shock.
I just keep coming back to the stranger rapist here. It's hard for a man not to know he is forcing a woman to have sex. A man who forces a date or a partner must, surely, be getting off on something more than just sex. I can allow some cases where it is lack of self control and/or a terrible misunderstanding of the 'banter' that so many men seem to think is harmless, but not all.
And, again, it comes down to power.
Because they can.
So, power in a very literal way - physically being able to force someone - and power as a means of achieving sexual gratification.
But there's also powerlessness as a motive to do something powerful. We live in a society that demands all men be alpha-males, but only allows a minority to achieve that. Of course there are some men who feel inadequate and powerless, and they may find the opportunity to be powerful quite irresistible. There's probably a bit of that in some stranger rapes and in some date rapes.
The criminal justice system hands the rapist another powerful weapon, of course. A very difficult ordeal in court.
And casual sexism means they'll probably be under the impression, rightly or wrongly, that their mates will approve. Peer approval is likely to be the main driver of gang-rape, especially amongst teenagers. And gaining peer approval is all about power, if you're in a gang.
So yeah. Dunno if that makes any sense.