The STDs you may get from sleeping around are only the tip of the disease iceberg. As I got older, I now have a morbid fear of all contagious diseases now. So even if I see someone desirable I might have a chance with, the odds are almost 100% I won't act on it.
Being in a stable relationship at least insures you aren't spreading some zombie disease horror from partner to partner and your own family. Even before microscopes and microorganisms were known, ancient people tried to practice good hygiene and sanitation, especially in the sexual realm. Because those who were stupid and didn't died. But with technology, even the stupidest people with little regard for hygiene or sanitation manage to keep on breeding like rats in spite of themselves and their true nature to be filthy animals.
And as was pointed out, is jealously natural? It sure seems so since nearly everyone seems to feel this way about their partners who they CARE about, regardless of any religious teachings that may be involved. But when you are in a relationship just for sex, the caring part usually flies out the window along with jealousy and then obviously monogamy isn't relevant to that relationship. And their kids are going to mimic the same behavior they see their parents engaging in relationship wise, so the same genetic cycle tends to continue through generations, either monogamous, polygamous, polyandrous or polyamorous.
And the undeniable proof of the success of monogamy in the human species is the fact that human sexual relationships that are closely related tend to favor genetic defects in the children that lead to sterility and deformities which results in a genetic dead end. This familial genetic factor is not at play as much in less complex species, so trying to compare a humans complex mating habits to a bird for instance, isn't even really a valid comparison at all, from a genetic stand point.