The equivalence is that children have first amendment rights (see Tinker v Des Moines) and speech delivered by the internet is still speech.
Porn may provide a suitable model: not all movies need age verification, so those can be viewed at any age. Some movies, however, do require age verification. Similar age ratings could be applied to apps. For example, Facebook only after 18 regardless of parent's approval.
Good in theory, but practically impossible. Peer pressure is too high for parents to be a significant barrier. If you were successful, please share how you did that.
Good thing that isn't what happened. It is called an "analogy" and is not a factual statement of equivalence.
The MPAA rating system and adhering to it is completely voluntary.