Banning children from uploading to large public sources sounds extreme but it could actually create really good market conditions for host-your-own services. A group of friends could have their own video host.
You mean like a containerized version of *tube people accessed as a service run for them, or encouraging people to actively host and maintain their own?
Maybe an ideal service would offer both— paid private and shareable containerized hosting and an open-source or free-download host-your-own option.