I've been thinking and it actually makes a lot of sense for new ways to be created to transfer money and pay for things (though I'm highly skeptical of having it operated by Facebook and of the ad-hoc pump-and-dump-prone and whitewashing-and-tax-avoidance-friendly properties of cryptocurrencies). But when you think about it, it's insane that transferring money is something credit cards and payment processors can regularly charge a fee of 1.5-3.0% on. In order to change some numbers in a couple databases... The marginal cost of this ought to be less than pennies. The only reason they can even partially justify this is because of fraud and credit, and the costs associated with dealing with that. But what if we had a way to transfer money between entities that mandated two factor authentication to prevent fraud, and sidestepped the whole credit thing by only working if you had the money? (or required that you took the loan elsewhere, so the account that actually transfers the money does not have to deal with credit at all). Verify that the person is who they claim to be, and that they have the money needed, then do the transaction - no more, no less. No chargebacks, no credit checks, no fraud checks. Why isn't this a thing?
The actual cost of processing payment is far less than 1.5-3% - especially with debit cards (which actually implement most of what you think "is not a thing") but even when dealing with credit cards and the necessity to include some overhead for countering card fraud and chargeback costs and whatnot, the total cost is far lower, below 1%.
How can I know this? Well, how do all these credit cards that offer cashback bonuses in the realm of typically 1-2% make this unbelievable feat of paying you for paying stuff happen? They pay for it out of the 2-3% that they get for the transaction. Let's take 2.5% as a middle ground and deduce 2% cashback, that leaves us with 0.5% from which the actual costs of doing the payment have to be covered - and the profits to be paid to shareholders, of course.
Also, Europe has this nice regulation in place limiting credit and debit card interchange fees to 0.3% for credit and 0.2% for debit cards. This regulation has been in effect for a few years already, and the only thing that disappeared were these 2%-cashback-on-every-payment cards (or similar offerings, like granting airplane miles of about the same value). Debit and credit card issuers seem to be entirely able to operate under these conditions, which means that their actual costs of doing business must be under these fractions of a percent.
The credit card companies' share of the entire economy is problematic, but few companies could handle the threats of fraud in e-commerce as well, for as little. There's a very harsh tradeoff between ease-of-use and fraud protection, and it's not an easy problem to solve. Doing it for 3% is beyond most companies' (or governments') capacity. It may provide the incumbents with a healthy profit, but few if any newcomers would be able to get their costs low enough to survive on that.