Restricting game downloads on iPhone should start with a simple question: what does the child actually need to use right now?
If the answer is a learning app, a video, or a call, then App Store downloads, game installation, app deletion, and purchase-related prompts do not need to be available.
Create a child-use setup with approved apps, then keep games and store access outside that setup. This reduces the chance of unfamiliar games appearing after a few curious taps.
iPhone Locker supports this scenario with app groups and system controls that can be adjusted before handing over the phone.