Context · YouTube
YouTube Kids is a genuinely different app with real filtering behind it, and it stops being useful at a fairly predictable point, which is when your child works out the main app exists.
What it does well
Content is filtered by a mix of automated systems and human review, comments are off, and you can set a timer that actually ends the session. For younger children it is genuinely safer than the main app and worth using rather than writing off.
Where it leaks
Filtering at that scale is never complete, so odd knock-off videos using familiar characters do get through, and they are aimed squarely at exactly this audience. The other leak is simpler: the main YouTube app is on the same device, in a browser, and on the television.
The moment it ends
Kids usually leave YouTube Kids because the thing they want to watch is not in it, and the exit is generally through a browser or somebody else's device rather than a request. Noticing that moment is more useful than trying to prevent it, because it is the point to have the main-app conversation.