"1. Human children need lots of care to survive; it is far from obvious that a man who has sex with many partners will have children who survive. As in many primate groups, the man who stays with one partner and nurtures the children could easily have higher reproductive fitness than the man who fucks everything that moves and then bails."
They're not mutually exclusive strategies. Many men pursue both when presented with the opportunity.
"2. From the perspective of reproductive success, there are obvious advantages for women who have multiple partners: not all men are fertile, more opportunities for support/food/protection, etc. Again, this is well documented in a number of primate species."
Different primate species have different sexual predispositions. One of the "obvious [potential] advantages" you point to is just as obviously very negligible. What proportion of men between the ages of 15-35 are infertile today? 1 in 10? 1 in 20? In the EEA, the proportion would've been even smaller. When balanced against the costs of detection (e.g. partner withdraws resources), it's unlikely that it would be in a woman's interest to take on an additional partner solely to increase the odds of pregnancy. On the other hand, if the prospective additional partner has better genes or could serve as an additional source of stuff, it might make sense to stray. The notion that some women enter extramarital relations with more attractive and/or wealthier men isn't exactly foreign to Western culture.
-- Luke