I don't trust the government to build a censorship apparatus and restrict themselves to only censoring the stuff I don't like. The 2nd amendment theoretically covers the right to bear arms, and yet, there is a raft of laws and agencies infringing that right in practice. How about parents actually do some parenting and monitor what their kids are doing online. Last I checked, neglecting your children is already illegal.
From a technical perspective, the only way enforcement of this would work would be for the government to visit literally every website on the internet, classify it, and either send law enforcement after the operators, or if hosted in a different country, block the site at the national level. It might start out as only blocking porn for minors, but in a couple decades, some crisis will happen and it will be extended beyond it's original scope. By that point, everyone will be used to having to get government permission to visit certain sites, and it won't seem like such an imposition. This kind of shit always starts as, "think of the children!!!!!".
EDIT: had same sentence in twice.