I can think of 2 reasons why a valid billing method is required for purchasing apps that are free. You will not be charged for free apps, but the payment method may still be required.
- Some apps or services are available only in specific regions. There have been users who change the region on their device in an attempt to get apps or services that would not usually be available to them. The billing method would be needed to verify your identity and would have to be from the same region as used by your device. Each region has their own App Store with apps that are available to be downloaded there.
- Even free apps may offer in-app purchases. Developers count on you liking the app enough that you will support their efforts and costs associated with developing an app by using an in-app purchase that they have offered. By not having a billing method, there is no hope for a developer to ever be compensated for the work they have done.