When you're rich, you have more to lose with indiscriminate sex. You didn't get to where you are by being indiscriminate. Unless you're a professional athlete, but they're not rich for the reasons we're talking about.
We're talking about Trump/Buffet/Gates/Romney rich, here.
Those people can't afford wrong turns with the wrong types of women. They have to protect their assets from would-be ambulance chasers who'd cry rape and take them for everything, or birth a bastard child that threatens their reputation. Once you get rich enough, your #1 asset becomes your reputation (your brand, if you will) and you mustn't tarnish it. You can make bad business decisions and recover. But if you tarnish your brand with a scandal, it can be impossible to recover.
Nasty random women will do that to a rich man.
So they have to overthink everything, which means they don't wind up having the level of sex a poor man can (assuming both are equally good looking). The poor man may have fewer total opportunities, but he can capitalize on a greater percentage for them, for he has little to lose. The rich man will receive more total opportunities (due to women being attracted to his wealth and power) but will have to discriminate against them, simply because he knows they want his riches and power. The rich man wants the sex with no strings. But the richer he is, the less likely he is to find a solution that works.
So, he gets married because he's starved for sex and companionship. And when he marries desperate, that's when he truly gets fucked.