

A lot of parents sadly lack any kinds of skills to use those tools nor even know that they exist.
As far as laws with potential to repress freedom of expression go, wouldn’t public government programs or campaigns to train & educate parents be a less compromising way to meet such needs without raising issues of liberty, privacy, coercion?

Not sure that part’s absolutely necessary: if it’s publicly promoted to the extent that parents don’t have an excuse (eg, time, cost, access) other than low willpower/interest they are reasonably accountable for, then the public has fulfilled its duty to empower parents to direct the rearing of their children while protecting everyone’s fundamental rights. However, I also think interested parents would popularly adopt voluntary solutions with enough public resources committed to promote & provide them in a major way. While the public expense may seem extra, I think the government’s duty to protect fundamental rights justifies the expense.
Another comment mentions legislatively commissioned studies that suggest solutions similar to yours, but broader & less intrusive. Recommendations included
They also stressed the importance of adult involvement to provide child supervision & teach children internet safety, information literacy, & skills to evaluate inappropriate messages. If the government had pursued these recommendations (it didn’t), I think it would have succeeded.
It’s also worth noting those & newer studies found client-side filters more effective than age verification for a number of reasons.
Though Australia isn’t the US, the US federal courts had an interesting opinion there: parents may always allow their children to access protected speech. Even with sex-related materials, the Supreme Court has stated
They regarded as constitutionally defective laws that impose a single standard of public morality. Instead, they’d allow laws that “support the right of parents to deal with the morals of their children as they see fit”. Laws that take away parental control are also impermissible.
In another decision, they regard & defend parental responsibility & discretion in leaving access open to children.
So, according to them, presenting such content to children ought to be left up to their parents, and laws shouldn’t infringe on their right to do that.