Interchange benefits merchants too - there's real costs associated with holding cash, and average cart sizes are significantly bigger for credit cards. They also miss out on fewer sales.
You may not value rewards programs but customers, card issuers and certainly those who operate those programs do. They're massive business. Frequently the only profitable part of a US domestic airline is its frequent flyer program - which gets the bulk of its money from credit card reward programs.
Credit card companies have even provided debtor in possession financing for airlines in the US by pre-purchasing multi-billion dollar blocks of frequent flyer miles. Here's when Amex did it for Delta in 2011. [1]
[1] https://www.eastvalleytribune.com/money/american-express-rea...