Why does my child have to go through the downloading app process again once I approve an app? Why doesn’t it just automatically download?

OP is still definitely experiencing a bug, it should absolutely automatically download once approved. Could you try this: Force restart iPhone – Apple Support (UK) and see if it helps?

You want your child to just keep downloading free and paid apps willy nilly, ad nauseum, automatically,until you owe Apple a ton of money in apps that you cannot afford pay for?

That is why these security features/safeguards/provisions are in place.

Best of Luck to You!