The problem isn't necessarily the branding on the cards. The transaction networks that carry the data from point-of-sale (merchants), to transaction processing facilities, to banks and back, are the problem. That infrastructure is run by Visa, MC, etc.

They also have a defacto cartel, not only due to owning the networks, but by complying with the very complex credit card compliance regulations. Combined with vendor lock-in for merchants and others, this creates a space that makes it obscenely hard for anyone else to join in. Just ask the folks over at Discover about that.