If we reframe this into societal terms, so that this doesn't get dragged into a "not all men want that" argument, why is it that most modern societies had/has rigid, monogamous family units? There are stereotypes for both promiscuous men and women, and clearly there's some degree of promiscuity in both genders. But the (vast?) majority of societies also adopted monogamous family units for most social classes. If men and women are promiscuous by nature, which forces led to the family unit in modern societies? Or perhaps that's just an illusion? How common was it to have a paramour anyway?

1) Societal stability

2) Most men are not capable of being promiscuous, even if they want to be

I think you meant to say that most men are not capable of polygamy? I would very much think that most men are capable of promiscuity.

By capable I mean able to execute. Most men struggle to find a single partner to be monogamous with, let alone multiple partners.

This is really not polyamory or non-monogamy in the way you’re framing it. Paying for sex outside of your marriage isn’t really non-monogamy in my book - it’s just sad.

The original argument is that monogamy is in place because men cannot get sex elsewhere. That is obviously not true. The point being that men also desire faithful long-term companionship. The ones who want casual sex or multiple partners still obtain that even in our monogamy-by-law society.

Define "many". I highly doubt that a majority of men have ever paid for sex, let alone having paid for sex while they're in a relationship.

Also, part of the allure of promiscuity is being able to attract/seduce multiple women. Paying for sex eliminates that.

Do people not use money as a proxy for power/status?

obviously nonmonogamous communities did not survive so what we see may be survivor bias. Nowadays however it IS becoming possible for nonmonogamous socieites to survive due to our superior technology. Hopefully there will be better studies out there than my office-chair evopsych.

monogamy != long-term partnership

Genghis Khan had 6 long-term wives. Most likely, the women were forced to be monogamous, while he obviously wasn't.

Wouldn't that mean that "mate guarding" behaviors would have to be assumed to be wholly due to social conditioning? https://en.wikipedia.org/wiki/Mate_guarding_in_humans

Don't some behaviors like that also happen amongst other mammals or other animals in general?

Ah... On the "men...want..." part, are you interested in what actual individual human men really want? Or just in a very simplistic, macho stereotype - which few men are likely to voice disagreement with, when it is repeatedly and forcefully voiced, in the context of a society where men often face harsh punishments (social and/or physical) for having non-conformist feeling on subjects like sex. And generally worse if they actually try to voice those feelings.

I guess I'm a martian then.

Then you define "want" in a very narrow sense, and there definitely is no evidence to show that it's "social condtioniting", nor that it's a desire shared by (nearly) all men.