The biggest reason I have my preference of CC first is points and to a lesser degree consumer protection.
I'm guessing you couldn't let me use Amex as a middle man between me and your service and not charge some fee, and I have a feeling I (personally) wouldn't be all that interested as the overhead of bill payment isn't that high (for me as just one person). Not to say it isn't an issue for some. I definitely know it was when I was younger, but I'm not sure how much of that was how available online payment was at the time.