Why can't I delete my payment method?

Wanted to give BF4 a go after being away from gaming for the past 9+ years so I decided to give the service a try. After things running pretty well on the free tier, I decided to buy a month of Ultimate.

Really impressed with just how well this plays, especially on my Chromebook, but I'm just not into gaming the anymore it seems. Downgraded my service back to the free tier and wanted to remove my payment info so I'm not charged again next month. While I can add additional payment methods and change the default, there seems to be no way to delete your only payment method, even after downgrading to the free tier.

Am I missing something or is this just shady?