Hasimir, do you have kids? The point here is not to suppress 12-year-old's sexualities: who cares if they have a secret stash of porn? Certainly there's no problem with them playing standard AW with *each other*. But would you really want to play a game incorporating sex moves *with your Dad* at 12? I didn't think so.
Leaving the sex moves in the game would produce exactly the result you predicted -- nobody would use them. So the driver would never have to prove their independence from anyone, the Hardholder would never have extra gifts to give someone they'd been intimate with, the Brainer would not have intimacy triggered a deep brain scan, and so on: that's all just out of the game.
The point of the Secrets is to KEEP that large part of Apocalypse World -- that intimacy between the characters matters, that it has mechanical teeth. So rather than insisting on keeping that intimacy as being literally sex, in a situation where the social contract at the table doesn't support it, the idea here is to replace that intimacy with something else.
Obviously, if people pick trivial secrets, it's not that interesting. The MC should coach players to make the secrets matter by asking leading questions -- "why is this a big deal? why haven't you dared to tell anyone?" Last night, people picked pretty interesting Secrets, each of which was an opportunity for the MC to bring things into play. No one actually got around to telling their secrets in the first session, but I think that's okay: they were on the horizon. Even in a game where sex moves never trigger, AW's sex moves are there on the horizon, signalling something about the game -- that sex is part of this game and taken seriously, that intimacy has teeth. Similarly, here, the secrets, though untold, were still on the horizon, signalling something to the players -- that they were the kind of people who had secrets, and might share them.