I'm not sure what you mean by saying that animals don't feel pleasure. Bonobos have sex roughly every two hours because it feels so good. Females rub their clitoritides together and engage in oral sex, sometimes preferring that to mating with a male.
And I didn't say why shouldn't we just let everyone copulate, I said, why don't gorillas and other species that fight for the right to mate with a harem of females not just go at it with everyone the way chimps and bonobos do?
Humans are still animals. And many, many human cultures do not engage in the kind of sexual monogamy you are describing.
Both my husband and I actively enjoy seeing each other having sex with other people - not from a kink perspective, but because it brings us pleasure to see the other one in pleasure. In fact, embarking on a polyamorous lifestyle has enhanced and strengthened our relationship with each other. In addition, group sex comes with a lot of bonding elements to it. It feels both incredibly natural and entirely human to connect in the same way that many other primates do when you throw off the cultural conditioning against it.
Sex is primarily for the physical pleasure and the social bonding aspect that it brings. After all, humans are a highly social species. And yes, of course, in humans it can have spiritual or other deeper implications as well, but that doesn't mean that there is no such thing as a "ticking biological clock," something that has become a kind of trope because it's so ubiquitous.
I make no assertions about intelligent design. The fact that your liver filters your blood or that the rods and cones in your eyes have a particular function has no bearing on how that came to be. Evolution serves itself, and not having your species die out is an obvious fundamental function of certain biological drives.