Facebook's potential advantage in this space is not that they have a billion users, it's that they arbitrate the identity of those users. And payment is inexorably linked with identity, especially WRT avoiding fraud.
Certainly it is a difficult market to enter, but a few billion dollars can buy you a lot of expertise, relationships, and time to build experience.
The reason Facebook should go into transactions is the same reason Willie Sutton robbed banks: "because that's where the money is".
The problem is that it isn't where the money is, not much more money than Facebook is already making anyway. Not unless facebook intends to commit theft. The money today is in selling digital goods which have a near zero transactional cost. Music, movies, games, books, etc. Not that it makes sense for facebook to get into that business either, necessarily.
I don't have the statistics in my hands, but I'm willing to bet that the transaction volume of nondigital goods is at least two orders of magnitude larger than the transaction volume of digital goods. A 1% cut of tens of trillions of dollars worldwide is worth quite a lot more than 30% of a few billions.
Granted, a worldwide payment scheme is a Very Hard Problem To Solve for many nontechnical reasons... but this is exactly the kind of problem that large, ambitious companies with lots of street cred should try to attack. If it was easy, everyone would be doing it.
Real world examples don't bear those numbers out. Look at Visa. 2 billion cardholders, $4 trillion in transactions a year, 80 billion transactions a year. And their revenue is only about twice Facebook's. Unless facebook becomes a merchant bank and convinces millions of merchants to use them they aren't going to see much higher of a per transaction profit margin. The math just doesn't add up.
If the business proposition was simply "make another Visa" then sure, the proposition would be uninteresting.
On the other hand, 2-3% of that $4 trillion is being consumed by the payment processing chain. Only a portion of it goes to Visa; the rest presumably go to banks and other layers of the service. Facebook potentially could, by virtue of being a trusted holder of identity worldwide, subsume all layers of this chain.
Look at it from this perspective: It currently "costs" 2-3% of a transaction to make a CC purchase. That's a huge dead weight loss. Is Facebook capable of using its brand, reach, and identity database to create a more efficient system?
2-3% isn't a dead weight loss, it's paying for very valuable things, especially fraud protection. You can't just magic it away.
Also, as I said, if facebook wants to step into the payments middle man role (which they could) they could maybe make as much as Visa does. If they completely reinvented themselves and turned into a global merchant bank AND managed to convince at least a tenth of all merchant account holders on Earth to switch to them THEN they could make some serious money. But the likelihood of that is precisely zero plus or minus a teeny, tiny margin of error.
In answer to your last question: no, no they are not.
Fraud is a massive problem in the existing payment system only because the architecture is horribly broken. The trust model is completely wrong. Nobody would design this system; we tolerate it only because of inertia, and because merchants are contractually required to hide these fees from customers. There's also an enormous regulatory burden to overcome. I'm not saying there still isn't a fraud issue, but it could be cut to a tenth just by changing the trust model.
My point is that Facebook is in a position to try building a new system, and the payoff is potentially enormous. Having a definition of identity that extends beyond a name and a cc# goes a long ways towards limiting fraud.
However, I tend to agree with you as far as Facebook's technical competence. This doesn't mean they shouldn't try.
As far as the chicken-and-egg problem goes, FB might do well to bootstrap a payments system in lesser-developed nations where Visa & Mastercard don't have such a lock on the market. A truly global payments system stands a good chance of eventually winning.
Certainly it is a difficult market to enter, but a few billion dollars can buy you a lot of expertise, relationships, and time to build experience.
The reason Facebook should go into transactions is the same reason Willie Sutton robbed banks: "because that's where the money is".