1) Those who are clamoring for age verification (generally on sites they never interact with themselves.)
2) People arguing fiercely against age verification and won't engage with any site who uses it
3) Most significantly, the large majority of people in the middle who can't be bothered to do AV and will just use another overseas website instead.
Even if the privacy can be solved (and I don't believe it can as someone fundamentally unwilling to upload my ID even once), that balance is basically the problem with trying to outsource the work to people who don't want to do it. We can already see that even privacy preserving solutions will not be used by adult site visitors in multiple adult site attempts to roll it out. The ONLY viable solution is parental filters on device. Anything that pushes the work to people who don't want it fails because the sites will just move overseas instead of losing the vast majority of their actual users. Or they roll it out and the traffic moves overseas, like data analysis has shown happened in UK.
You just can't solve the problem by pushing the work onto everyone instead of tackling it at its source. Rather than try to lock down the entire Internet, which will never happen, lock down child devices.