This is not an exclusive or. Corporate lobbyists from social media have a real incentive for pushing age verification and attestation. They benefit from public outcry and popular movements for age restrictions online, while also presenting age verification as the only solutions to the problems causing that outcry (which is to say, largely moderation problems on their own websites).
And I think the problems with social media for children have little to do with moderation. It's more about the typical ails that even 'good' social media would entail: FOMO, image crafting, amplification/streamlining all typical stuff that happens at all schools - bullying, rumor milling, and so on. To say nothing of the general effect of people becoming zombies to their phones rather than actually interacting in person as much.
>Age verification will be a significant loss for social media companies. It's going to push plenty of people away, and it provides no information that they don't already know to a reasonably high degree of certainty.
It may push some people away (though with the centralisation of the internet, I think this is easy to overstate), but the social media companies probably aren't that worried. Their bigger threat is actual legislation and punishment. Age-gating prevents the government from coming down on them for bad moderation, since they can just block users from accessing anything that might need to be moderated otherwise.
The possibility that age verification will actually give them more data or let them track you more easily is a nice little plus, but this is more stick than carrot.