Having state-mandated software running on every device sounds like a much more invasive solution, and more easily turned against device owners.
Whereas making online service providers responsible for the content they offer is more lightweight for the end user and is more consistent with how it's done offline, like with age verification for certain types of purchases.
No, it's merely included on every device sold (at least those with preinstalled operating systems), for the benefit of lazy parents. But it is software like any other, that can be completely removed by the owner (that is what "fully in control of the owner" means), and is open-source on top of it.
Whereas making online service providers responsible for the content they offer is more lightweight for the end user and is more consistent with how it's done offline, like with age verification for certain types of purchases.