Hey there dfallr,
We'd like to help! The first thing to clear up would be that no app downloads from 'iCloud'. All apps download from the App Store. With that said, any apps you've download in the past can be redownloaded again from the App Store.
Regarding your question about blocking your child from downloading a previously downloaded app, there's not an option available to prevent them from downloading a previously downloaded app on their iPhone. With that said, you can enable Settings > Screen Time > Content & Privacy Restrictions. Then, you can select which apps are allowed under 'Allowed Apps' in the 'Content & Privacy Restrictions' screen.
Any product feedback you'd like to submit to Apple for consideration can be submitted here: Product Feedback
Cheers!