Why is my iPhone trying to charge for free apps?

It’s trying to charge me for free apps

No, but if you purchase something then you have to pay, if you don't pay then you owe that amount to Apple until you pay.

You can download free apps, but you may need to have a valid payment method on file, even if the app you want to download is free. 

You can have a credit card / debit card on file and an Apple Account balance.

If you have set your Apple Account balance as your default payment method, your default payment method will be used first by Apple when you need to make a payment.

Free apps has also In-app pruchase.

See -> Buy additional app features with in-app purchases and subscriptions

Buy additional app features with in-app purchases and subscriptions

See also -> Apple Media Services Terms and Conditions

Legal - Apple Media Services - Apple

You need a valid payment method in your app store account, even for free apps. It won’t charge you for the free app, but the payment method must be attached to the account. Under some circumstances once you have downloaded a free app you may be able to remove the payment method, unless you have any apps with in-app purchases or that offer subscriptions.

Mine already had a valid payment method and is trying to charge me $5 for every app I try to download