Because Google clamped all different concerns about kids on YouTube into the one feature without differentiating between videos with kids and videos for kids, and there was concern about recontextualisation of videos with kids as pedophilic erotic by including them into public playlists with inappropriate names and descriptions.

COPA says something like even if the user identifies as an adult through an age gate you are liable for the anti tracking stuff if the content is kid friendly/targeted at kids.

I don't know why the Watch Later feature is disabled for kids videos, but I think it's pretty common for kids to use their parents' accounts, particularly with device sharing (family iPad, or kid uses parent's phone).