I'd be glad if you could share some of the games you approve of as my child is recently more interested.
And what are 'skinner box' games?
Usually achieved by a stamina system (You can play up to 5 levels in 30 minutes, or play another immediately by paying), balancing play so playing without "Premium" items feels sluggish and uncompetitive (but not so sluggish that the game is unfun), and having a lot of gambling style elements to overcome the first two (No gems? You can spin the prize wheel once a day! Also, you logged in 3 days in a row! Have some gems!)
A recent one was "Star Wars Force Arena". You really need to shell out to play, but you get these virtual "cards", sort of like electronic Pokémon cards that have characters and weapons. Usually they give you junk characters, but once in awhile you get something good. Your have to connect in specific time intervals to get more cards, and we discovered that my son was actually waking up early to claim his cards.
Other nice games come from Toca Boca. My son and his cousin like to play with "Hair Salon 3", where you basically cut and style hair -- they have little contests to make wacky looking people.
The physical Apple Store is actually a good place to discover new games. They change it demos every few weeks and the staff is often very knowledgeable.
A tremendous amount of games on phones are either glorified slot machines, or a normal game with some kind of slot machine tacked on, such as a loot system.
Some even produce loot that can be traded for real money...
You have to vet every game now.
You need to be very careful with modern mobile games. I'll let my son play minecraft, do the "endless learning" games, Dr Seuss, movies, and a few other selected games. You need to avoid the skinner box games.
Generally speaking, if it has a franchise endorsement (Star Wars, etc) it's garbage.