As a fellow parent, I cannot recommend Apple Arcade enough. My son is only allowed to play games that come from AA. These games aren't allowed to have any ads or in-app purchase. In return, you pay seven measly bucks a month (though I have it included as part of a package since we use iCloud and Apple Music and Apple TV+ anyway).
The games in AA are either made for Apple Arcade (some great indie type games) or, very commonly, they are basically 'de-fanged' ones from the regular App Store, with all the IAPs and ads ripped out. Where there is an in-game currency that normally is scarce without paying, they'll either just give you a bunch of it to start with, or you will earn it naturally while playing.
I agree with you that the number of ads and purchase-pushing mechanics in all regular App Store/Play Store games is insane. It's all because a few whales who do buy these purchases are what pays for the whole thing.
Know of an equivalent for Android?
I'm leaning towards letting the kid play games only on an XBox and never on the phone. Even if I get rid of the ads, I don't want the games to be accessible wherever they are. Whereas with a TV, they need to situate themselves in a dedicated place to play games.