Hey there WaltSe,
Thanks for reaching out to Apple Support Communities. We're happy to provide some assistance.
You do have the option to prevent App Store downloads. Check out this helpful resource under "Prevent iTunes & App Store purchases" section: Use parental controls on your child's iPhone, iPad, and iPod touch - Apple Support
"Prevent iTunes & App Store purchases
You can also prevent your child from being able to install or delete apps, make in-app purchases, and more. To prevent iTunes & App Store purchases or downloads:
- Go to Settings and tap Screen Time.
- Tap Content & Privacy Restrictions. If asked, enter your passcode.
- Tap iTunes & App Store Purchases.
- Choose a setting and set to Don't Allow.
You can also change your password settings for additional purchases from the iTunes & App Store or Book Store. Follow steps 1-3, then choose Always Require or Don't Require."
Keep us posted.
Have a great day!