I don't think you have to destroy internet anonymity. Just fine parents like $25 or $50 bucks every time anyone can link their kid to social media use. Give people rewards for reporting it or something. Even as little as driving kids towards platforms that incentivize anonymous interaction over real name and face stuff is probably enough move the needle. That said, I think social media use has a very overlapping relationship with allowing kids unsupervised and/or frequent and lengthy use of tablets and phones from early ages, which I suspect is also destructive.
But then they will contest the claim, it will then have to be investigated, and that will cause huge amounts of pointless busywork that will amount to no clear evidence. Not worth it for such a small fine