The best thing a parent could do is download a set of approved videos and use a local playlist.
The easiest thing to do is just allow them on youtube no filter.
The middle ground is the play app. Weird stuff sometimes get through but usually it's more someone dressed as a pretend princess. The good thing it's never really a murder scene or something equally as horrible (which could popup on youtube.com).
What would you do as a parent?
I would avoid youtube unless you setup the video until 7 or 11. After that it depends on the child.
The one big thing "For Kids" has going for it is the pro-active identity. Rather than feeling like they are missing out by not being an adult, they instead feel like they're picking the thing that's special for them.
"We've found adults and teens like different parts of youtube and use it differently. We want to make it the best for you. You can switch at any time, but tell us what best describes you:
* I'm an adult
* I'm not an adult.
"
youtube has this "for kids" app which came out after I first started pointing this difference in earnest around 2013, (https://play.google.com/store/apps/details?id=com.google.and...) but it's not right and they clearly still cater their main interface to the habits of children who watch the same video hundreds of times - the insane repetition is a part of learning nuance and subtly in the context of content they don't have to actually pay attention to. It's all about learning the meta, super important. They know what happens, it's the silence in between they're excited about - that's the nature of play.
This app instead silos the kids into a playskool interface, great for people under 7 or so, but like our playground reform, we've made it completely unappealing for the 8-22 or so demographic (when I was a kid and there were ziplines into a bank of tires, you bet there were 20 year olds lining up to have a good time on those, we all have a need for play; freedom to err wrapped in relative safety).
Instead, it's data-driven UX for adults and data-driven UX for children - it's about separating the data, not a PTA-acceptable UX for overprotective parents.