I think so. Among other reasons, those ads were deliberately included in the app by the people who created it (and now have explicit responsibility over the content of those ads).

Since parents trusted those creators enough to give the app to their children, that's something.

I'm curious what keeps "first party" analytics/ads just phoning home and doing the third-party transaction server-side.

Apple's banhammer, should the public ever catch you in the act. (I guess.)

And their ban hammer is not terribly sophisticated either. They find one ad that is the same, or similar to, an ad being served someplace else and WHAM!

Unless you've got money to burn, don't try to be nickel slick with Apple. Learned that the hard way.

Likewise are first-party analytics better than Google Analytics?

Some people definitely think so

What defines first or third party?

The creator of a kids game is first-party, and can manually place ads within their own app. Anybody else is third-party, and is not allowed.