The nice thing about a credit card rewards program is that it requires zero mental effort. Some people like spending more effort to do churning or whatever, but I make the same computation in that case and conclude that the extra money isn't worth my time.

Paying without a credit card is just supporting the credit card fees of those who do pay with one. The price is the same, but you often get 2 or even 3% cash back (depending on offers).

Anyone financially responsible (i.e. that won't get enticed into carrying a balance by the opportunity to get cash back) is leaving money on the table by not using a credit card (with good rewards).