Obviously in theory stock Android can do that but they don't really take child locks seriously because they have the wrong threat model for it - they think "it only has to be securish because most children aren't going to be smart enough to circumvent it and it's not serious if they do anyway", instead of "it has to be actually secure because you only need one smart child out of thousands to figure out a bypass and it is serious because it affects peoples lives".
So maybe you could have an Android distro where it literally white-lists a few apps and servers at the OS level.