This is the problem, its just convenient and free. People are not thinking about the costs to the end consumer - which in this case is our children. I don't really fault PBS, but I do fault the advertising companies for our general lack of privacy and control over our own data. I also fault the politicians for turning a blind eye to it. I hope Apple's new strategy to go after privacy pays off in a big way and more companies fall in line with it. Or at very least more people begin to think about the trade-offs before blindly injecting google analytics into everything. Self-hosted analytics that does not feed into an advertising giant is not unobtainable goal.
Depending on the apps, you could make some age assumptions of the kid too. Even more, perhaps extrapolate the number of children in the household based on the age-ranges of the apps and the behavior of how they are using the apps. A 3 year old and and a 5 year old are going to have very different usage patterns. The number of children and their age ranges could be a very important metric when considering targeted advertising to the parents. The fact is, this information is used against the consumer to manipulate them into doing things they wouldn't otherwise do - click an ad and perhaps make a purchase. Any bit of information to further that goal will be used, even better if its information about the children since that's a major purchasing factor for parents.
In fact, so many apps embed these analytics frameworks, that it's possible to make an almost complete picture of what a device was used for every day, including location information, etc on the back-end.