It's a bad way to handle it. But you can't deny they will in fact have sex if they cheat

That's not something you can disagree on, cheating implies sex so this person, as shitty as they may be, will solve that withdrawal.

I never claimed it was a moral solution. I never claimed that it was an optimal solution. I claimed it was a solution. And it is.

And yes, if killing all the poor people meant no poverty, it would be a solution. Not a solution we would choose. But a solution nonetheless.

What you're thinking of, is a slightly different set of criteria. "I want to have sex and not hurt my partner" =/= "I want to have sex". And not everyone has perfect morals.