Why do I have to pay for app downloads on Apple but not on Google?

You are not charged at all to download anything that is noted with the "Get" button in the App Store, and frankly there are more free downloads then there are paid downloads. Many times those free downloads will also contain in-app purchases to allow you the opportunity to try the app out before paying for additional features/subscription.

Developers are not spending their own time and money to develop apps and continue to update them without any way to monetize their efforts. I suspect you would not be spending your time and money to do that either. For any app that does not require any form of payment, you must wonder how they are making their money. Are they selling your personal information to advertisers?

You will need a valid payment method on file to use the App Store and it may be possible you are confusing the prompt to add your payment method thinking that means you are being charged. You are not charged to download any of the free apps in the App Store.