Originally Posted by DaDOKin DC
I think banks don't accept them because that's the way they've always done it.
Kind of, but there's a very valid reason for the policy.
A mortgage is usually the homeowner's largest debt, and the banks don't like the idea of you paying for secured debt (mortgage) with unsecured debt (credit card). Yes, you may be doing it just for the miles, but most people don't pay off their credit card debt monthly (another discussion entirely).
In any case, it is impossible for the bank to know if you are using the card because you don't have the cash or just to get the miles. By requiring "cash" payments they get the earliest possible indication of any potential problems with your mortgage.
It's good business practice on such a large debt. As such, miles for mortgage payments remains the Holy Grail of free travel.
I suspect that some marketing department will eventually work out a program, but probably the tradeoff will be a higher interest rate or service fees, as is currently the case with all the miles for mortgage programs now where you get miles when you consummate a loan.