Visa and MasterCard are basically branded, proprietary protocols. They regulate how card issuers (banks) and card acceptors (PoS and other banks) work with each other.

You can remove those proprietary protocols, replace them Bitcoin. Your card in such situation is replaced with multi-signature Bitcoin wallet and have most advantages of current system without it's greatest problems.

What stays? Third party (ex-bank) is still capable of providing you mechanisms that are there to protect your money in case of theft of your wallet. What goes away? Third party (bank) no longer has control over your money. They can't steal it or freeze it. They can't prevent you from using it.

Added value? Since you no longer need Visa INC and you can freely switch between financial services providers (ex-banks) your costs go down.