Apparently on Youtube you can't put kid's content on your Watch Later list or any other. Why?
Don't know the specifics, but Youtube made some changes to how stuff flagged as kid's content is treated not too long ago. If you watch it on a phone or tablet then it won't play kid's content in the miniplayer mode either.
Might be something to do with the flak they've been getting for letting shitty content keep getting highly recommended by the Youtube Kids algorithm.
The core point is that the entire thing people are asking for isn't viable. We want to upload whatever videos we want, instantly, no restrictions, yet somehow have everything perfectly moderated, for free. And we don't want the channels we like to ever get any content strikes, only the channels we don't like. The concept just doesn't work. It's a crazy thing to expect anything like that to work. Either they're too draconian and people get pissed that their favorite channel or videos got taken down and/or they're too lenient and they should dalek-exterminate all the channels we don't like in a hail of fire. At the same time.
People aren't willing to pay what it would cost for human moderation for Youtube. The same people who generally say "youtube should do something about all this bad content" also tend to go "oh hell no" to the idea that they should, for example, have more adverts to pay for something like that. The reason it works for broadcast TV is that everything is curated and from known sources. Something where people just upload "whatever" can't possible by cleaned up to broadcast TV levels of sanitization without forcing people to pay a lot more for the service, one way or the other. The only way it would be viable is if they end up with only "approved channels" and have a very low bar for striking out and getting your channel canceled.
What does this have to do with a Watch Later list, though?
Because, they've had issues with a small amount of inappropriate kid's content then instead of having humans clear it up they've basically quarantined everything labeled "kids content" off from everything else. So you can't include it in lists or any of that. This is probably to prevent you making a list and include some kid's content along with inappropriate content then saying "look kiddies watch my playlist". The fallout of that is that you can't even include kid's content in your own personal Watch Later list.
So you'd think that the solution would be to flag inappropriate content and remove that, but that's not going to work, due to the ability of someone to upload stuff that hasn't been filtered/curated and then include that in a list which also includes kid-friendly stuff. So what they did instead is flag
all kid-friendly stuff and put that in a separate sandbox. Which makes sense. There's now a white-list of kid-safe stuff rather than a black-list of non-kid-safe stuff.