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.
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.