if you have a phone and you want to download something onto it you need to sign in to the app store and provide your credit card. And it doesn't MATTER if you download it for your kid, the app store has your stuff. Apple at least has a setting so you can mandate that you log in again shortly after. But again, setting, not default, hard to find, not advertised. This is a problem with basically EVERY parental control scheme I've ever seen, it's hard to find, it's not advertised, it's not presented the instant the app/game/store is aware this product is being acquired for a minor.
As for the child buying things without the parent knowing, you ever heard of this thingie called "allowance"?