All these middle aged women who have no skills due to raising children would be able to support themselves by giving old men handjobs.
Keeping prostitution illegal helps save marriages . also has the added benefit of making it harder for the husband to cheat on payday.
I might just be dumb, but I have no idea what you mean by “no skills due to raising children,” or why the lack of sex work would make it so they couldn’t support themselves, given there are single parents right now that have jobs that don’t involve sex work. Are you just saying a lower legal barrier to entry would make more child-rearing single parents seek employment as sex workers because it would pay more than the lower paid work they otherwise typically get compared to non- child rearing parents? Also, if these single parents are married and tend the house, that they have lower paid work is moot if their partner makes up the difference for the household. It’s not clear to me whether you are referring to single parents here or not tbh.
It seems to me, even if people in general were more likely to engage in sex work when it’s legal, this would have more of a chance of affecting the marriage rate itself rather than the divorce rate. And even that not necessarily.
Most people who cheat are not opportunistic cheaters, i.e. are not people who were simply waiting for an opportunity to cheat to come along. Getting paid creates an opportunity to go to a brothel, but it doesn’t induce a motivation to cheat the way, say, meeting a cute coworker that you really get along with might. Which I think is more common.
The three scenarios that would have one pay for sex is (1) a desire to fulfill specific sex acts that most people would not or which are socially stigmatized, (2) a need to recuperate sexual confidence, or (3) simply having a more short-term hedonistic sexuality while also being lazy about dating (though in that case, they would be more likely to just propose a different relationship model upfront as opposed to straight-up cheating through paid sex, if different relationship models weren’t stigmatized). A lot of these are also potential reasons for relationship counseling or break-up independent of whether sex is paid for.
My own hypothesis is that, at best, legalizing sex work would lead to higher incidence of payment for sex as a reason for break-ups or divorce due to it allowing ease of access to sex, but would have no effect on break-up or divorce rates themselves.