The problem here is Visa/MC/Amex etc. Since you almost have to accept credit card payments these days, you're stuck with their terms. Since the banks all provide credit through these card providers, there's very little competition.
There are numerous ways to virtually eliminate CC fraud but the card providers aren't interested in taking those measures, and neither are the big retailers. They are happy to accept the ~5% loss on chargebacks, because credit card users spend something like 30-40% more per transaction than cash payers.
What we need is a competitor that disrupts credit cards altogether, not just merchant processing. Eliminate VISA and MC, who are basically skimming 2.5% off our retail economy. Cards are obsolete anyways. The processing side is obsolete, we don't need terminals that dial into a central processing machine, we can use the internet. The credit side (banks provide the credit line you get on your card, not Visa/MC) will take a bit more work, but we can combine it with the rise in peer to peer lending: you seek a credit line from a crowdlending site, not Chase bank.
But the OP is NOT the merchant... PayPal is. I do not think that the fundamental problem in this case is the credit card system. (Although there certainly are OTHER problems with the credit card payment system that make it tempting to disrupt - but nearly impossible to disrupt because of entrenched powerful interests.)
Not only that, they are making it extremely inconvenient to have any sort of communication with them
As soon as a payment touches any of the existing networks, it's at risk. The only way to fix it completely (or at least significantly improve the situation) is to have a system that's completely isolated and properly secured; i.e. every payment authorization requires true multi-factor authentication.
This claim doesn't make much sense. For example, an economy with RGDP 150,000 units, of which 2.5% go to Visa/MC, is not worse off than one of RGDP 130,000 units, of which 0% go to Visa/MC.
Now, nearly everyone has and uses multiple visa or mc branded credit or debit cards, yielding trillions in transactions, making billions for Visa/MC.
In short, they've grown much more profitable due to their scale and none of that has value has been returned to businesses or consumers in via rate reductions, AFAIK.
Of course, there are other ways to stop fraud which you'd want to do as well.
They could charge for "Verified by Facebook" services. Hell, they could replace eBay and PayPal while they're at it, not to mention AirBnB, CraigsList, etc.
They're stumbling around looking for a business model as it is, I don't know why they don't get into this. Sure, easier said than done maybe, but if anyone can do it, it is Facebook. Becoming the one site that has the single largest repository of known internet identities within it is the hard part.
So bizarre to me they don't move into in a serious way. ecommerce
Is that workable? Quite possibly. Is it probable? Probably not.
Edit: Spelling