The knowledge that custody will automatically go to the woman, I am sure, is a major driver into why many more woman initiate divorce than men
In humans we are subject to habituation. You will eat more revels than maltesers in a sitting. You get used to the taste of the maltesrs, which all taste the same, quicker and rewards becomes less. Revels constantly change taste and so you gain more pleasure from them and continue to eat them.
I think the same happens in relationships and we'd have more varied, and rewarding relationships, if people had multiple lovers (Revels) at the same time.
Can you ever stop people cheating 100%? No, of course not. As long as there is reward some people will do it. Even the opening book of the Bible, Genesis, is about people cheating (eating the apple) due to temptation.
I do think reconising monogamy as merely a subset of the rich breadth of human relationships would give people more fufilling relationships and that would naturally lead to less cheating.
The numbers are stark. 9% of mammals are monogamous, 29% of primates and before western imperialism 83% of societies were polygnous.
For full disclosure, I myself am in a monogamous 10 year marriage. Of course there are temptations and ups & downs but have been faithful. The opinion I came to is after reading all of the heartbreak on MN and it just became obvious to me, monogamy is to blame in almost all cases.