The power that comes from being rich, well connected, parading powerful friends (even judges, politicians, financiers, and so on), aides, bodyguards, the means to have them beaten or killed if you want to, and so on? The power to get them fired from their jobs? The powerful to do "Eyes Wide Shut" level shit to them and them knowing it?
Or you expected some magical power that applies to every old rich person in any situation between them and a young woman?
Sorry, that seems extremely unlikely. I find it shocking that you think that way.
Just because somebody is rich also doesn't mean they can simply destroy other people's lives at will.
Btw I have personally witnessed for example young women courting old professors, who certainly didn't have any power to destroy their life. They did have some power to further their career, though.
Expect: yes, I think in most cases it is simply that the young women expect some advantage from the rich guy. Maybe just material things, or maybe just more fun. Maybe they enjoy riding on yachts more than riding on skateboards, or whatever.
I have seen many young women court older men for various reasons.
The term sugar daddy comes to mind.
One can question the basis of such relationships, but I think it's a huge stretch to suggest they always arise out of force or coercion.