Finally, someone realizing that kids' apps MUST have no ads and no way to exit (home button aside). My kids like several apps (Talking Cat & Angry Birds in particular) but keep handing it back to me to fix because a stray tap sent 'em to the App Store or some web page.
I think that creating some sort of "collective marketing" term or group maybe for kids programs that are like this would help reach an underserved market -- someone vetting iOS software and certifying that it is "Kid Friendly" (no ads, no IAPs, no way to exit other than home button, state clearly saved, etc.) would help parents quite a bit. You could charge developers to be listed in a directory (or do it as a public service) and sort of further curate the App Store, as a lot of the kids stuff in it is frankly exploitative and also frankly, not fun.
That sounds like a great idea but definitely not something I'd relish putting time into. Seeing my kids play games I've made for them is satisfying in a way curating apps could never be.
I think http://momswithapps.com/ comes quite close. A curated list of apps specifically for kids. It also doubles as a marketing vehicle for app developers.