It is exactly because we cannot trust parents to moderate what their children do online that these laws are coming up.
I disagree. The reason we cannot trust parents is because we are not making them responsible in the first place.. there's not a system in place to assign them responsibility regarding the child accessing places it should not (if we do really think they should not).
So if by "trust" you mean "blind" trust with no accountability, then well, we can't "trust" NOBODY, not just parents.
The problem is that instead of controlling the bad parent, we are trying to control everyone else to try and child-proof the world.
States require that you get a license, take a test, follow road rules, get your vehicle inspected, and many more requirements. We have these requirements because we know that we should not let an untrained driver on the road.
The reason I removed it is precisely because I expected this kind of misunderstanding. You are assuming that in my comparison getting a license is comparable to a sort of age limit permit, but the way I framed my comparison, the equivalent of "getting a license" would be educating the parents and keeping a "parental license". The parent is the bad driver.