The safest solution would be to download a list of videos from Youtube and run them locally as a playlist. Of course, that's not a solution that would work for most parents, or Youtube, or content owners, or probably the law. Second best solution would be curating a personal playlist of videos and to make certain children are always watching under supervision. Third best solution would be, ironically, preferring children's television over the internet.

As I understand it, Youtube isn't profitable for Google, and a lot of their decisions wrt their algorithms seem focused on increasingly desperate attempts at wringing some semblance of solvency out of the platform, so I wouldn't expect them to be very willing to work against their interests right now.