I think I'd pay something for the convenience of not carrying cash and the ability to shop online with customer protections.
But, anyway, the float is really not something I care about. In fact, when I have cards with good rewards (like my Schwab) and not enough credit (see my report of my US mint coins) I often end up paying a chunk before the bill comes just to free up space and get more rewards. The float amounts to zilch, especially with today's interest rates. But the rewards are huge.
Next, I assume cc companies will be happy for our business with no fees/penalties/interest just because they get a nice interchange fee.
Finally, as a merchant, I'm always surprised that the largest portion or our charges fall at the "qualified" rate meaning these customers are using no-reward cards, which cost us merchants less to process. They're literally leaving money (or miles . . . ) on the table.