Mastercard/Visa aren't paying the rewards (that's on the issuing bank), they're not doing much fraud protection (again, largely the issuing bank), and they're not responsible for any of the defaults or payment issues (you guessed it, the issuing bank).

The issuing bank sets interest rates (and late/missed payment fees, and penalty rates, etc.) to cover at least the defaults and payment issues part.

Right, but the issuing bank splits the percentage fee with the payment processor. Again, this brings up the point -- with the issuing bank taking care of all that, what is the payment processor doing that realistically costs the other 50% of that percentage fee?

If you look at Visa's margins -- it's pretty clear the answer is: not much.

I have heard running a "cartel" a few times in this thread. I don't understand this term. Could you explain what you mean by that?

A cartel is when a few organizations control something of economic value and act as a single entity in the market. For example, the 1973 oil crisis was caused when OPEC proclaimed an oil embargo. OPEC, controlling the oil market, acted as a group to greatly reduce the supply of oil to the United States (and other ally countries) for political purposes.

EDIT: In this case, payment processing is controlled by a few organizations. They have agreed to raise their prices at the same time, instead of free market style competition for the lowest price. They can do this because very few companies can do payment processing and it is very hard to become a payment processing company.

I'm pretty cartel has in English the same signification as in French