I think you've done a great job identifying the three main options and why two of them (parents, censorship-by-default) just will not work. That leaves regulation; the only way we will prevent children—or anyone—from coming to harm is to stop companies from producing this harmful content in the first place.
And what happens when those representatives decide things like rainbow flags being a crime or so much as mentioning the existence of trans people in front of a kid is equivalent to a sex crime. The US has states pushing legislation to make abortion a crime punishable by the death penalty while also using flock cameras to track people traveling across the country to places it's complete legal to do so. But yeah let's give those people a way to tie every website that woman may view while searching for a safe option now directly linked to her I.D. or that adult searching for gender affirming care is now outed because their ID is linked to the site. So when states like Kansas legislate all trans people's drivers licenses be revoked they can just say okay who in the state has looked at transgender healthcare related websites and have a list of people to go after.
Either that, or just accept the harm.