The first thing that would happen is they would cut off all your service.
If you are relying on them for something other than the thing you don’t want to pay for, this becomes a problem.
For example, I disputed a charge with my CC from the Apple App Store when I was charged for an app that I shouldn’t have been years ago. They immediately cut off my access to the Store. Other apps couldn’t update, OS couldn’t update, couldn’t get new apps, etc.