How would you have an affair if you're politically and economically powerful?

You trade money/favors for discretion from the smallest number of people possible, with the unspoken implication that if they betray you'll spend at least as much on inconveniencing them afterward.

Call up the local high end madam and ask for a "date".

Maybe some of them fear that using professional escort services make them bigger targets for blackmail or their information will be used to cut deals when the escort service is busted. Also, some may be looking for more than sex with professionals.

Cucking has existed since forever, for both the poor and the wealthy.