If indeed the push for age verification is being done under false pretenses as you suggest, then one should propose solutions that accomplish the stated goals while preserving privacy. Either the solutions will be accepted, or the people advancing false pretenses will be forced to come up with new false pretenses, which will weaken their arguments. Either way is a win.
> then one should propose solutions that accomplish the stated goals while preserving privacy
Solution: sites and apps optionally provide metadata suggesting their content/age-appropriateness, parents locally configure software to look at that metadata (including what to do with things that don't have metadata), or they don't, depending on their parenting style and the maturity of their child. Done. No laws or identification or invasive measures required.