There are two ways to get a giant pool of people using your payment system: start with payments and then get giant, or start with a giant pool of users and then add payments.
In the first case you'd have to start with a tiny, specialized payments market that you could then expand. The second case would be Facebook creating their own credit card system. Which they could probably do.
I'd recommend starting with a specialized payments market. That's how credit cards themselves got started. And you can't create Facebooks for the asking.
Would a company such as Facebook even want to go solo in being a credit provider? I don't see it. I do see them partnering with one of the big credit providers to create a FBCard. Then they could say that to use or purchase FBCredits you must use the FBCard which would also be a normal Visa/MC which could be used in any regular bricks and mortar place (with FBCredit rewards?) Imagine the data mining they could do on that! Now you have a FB user buying FBCredits for games/whatever AND they know what restaurants you frequent, what groceries you buy, if you smoke or not, etc., etc. And they would be able to do it all without the hassle of setting up their own credit department and collections issues. And they could probably do it so that a parent could sign up their under 18 kids for the card so the CC companies would love to get in to that market!
Square was my first thought, too. Yes, they could most certainly take on MC/Visa/Amex/etc. Maybe that is why Visa invested in Square? You have to get the POS units into retailer's hands. Then, at the same time, you have to get consumers using it. Where square differentiates themselves from the competition is that they make it very easy for anyone to become a POS node.
Now, the difference between Square and the CC companies is that square is really a gateway to those CC systems and not a credit provider themsleves... BUT once they have traction with POS merchants and acceptance by consumers could they start their own credit department? Sure. Would they want to? That is another debate. I'd wager it's much easier and still very profitable to be a gateway taking a small slice off each transaction than it is to be the credit provider.
In the first case you'd have to start with a tiny, specialized payments market that you could then expand. The second case would be Facebook creating their own credit card system. Which they could probably do.
I'd recommend starting with a specialized payments market. That's how credit cards themselves got started. And you can't create Facebooks for the asking.