Good question. A few months after the dispute process has begun, or at least after the debt has been cancelled, the credit card institution will close out that account. So no, that card will not be useful anymore. As a matter of fact, that institution would probably not want you again as a customer. After all, they're making a pretty lucrative racket by pretending to loan money when nothing -- not a penny -- EVER came out of their accounts to ANY credit card customer! So when they realize you're not going to play that game anymore, you're no longer a viable source of free money for them.
They can't prove that they didn't commit fraud . . . and so that is why they will let the debt go away when you challenge them head on. But on the other hand, they're going to keep their free gravy train going as long as possible. Customers who wise up to it are no longer welcome.
Further, in good conscience, it would not be ethical for the customer to deliberately create credit card debts and then cancel them, knowing in advance that it is a fraud. The action outlined by the Liberty system allows you to act in good faith, showing that you have learned about the fraud only AFTER having already unwittingly allowed the so-called "debt" to exist for some time, and after having mistakenly honored it by making payments to it.