While I haven't done a lot of research in this area, I would suspect launching a new credit card company is just a massive amount of work, very different from launching a new web app. You're obviously going to be subject to a lot of banking and capital regulations; you're either going to have to be starting an actual bank or you're going to have to partner with (at least) one, for instance. Then you have to figure out how to get businesses to start accepting you. "This card works everywhere that happens to have a Square-based point of sale system" is not going to get you to be the next Visa. It's not even going to get you to be the next Discover.

While Simple was trying to launch a new bank, not a CC processor, their experience is probably informative here -- they're successful by some measures, but they failed at disrupting the industry the way they wanted to. (I'm a Simple customer and have been on the edge of switching back to a conventional bank for over a year; it's mostly just inertia that keeps me there.)