There has been nothing stopping US merchants from offering cash and/or debit card payers a discount since Oct 2011.
https://www.ftc.gov/business-guidance/resources/new-rules-el...
Most merchants are betting that people paying with credit cards are willing to buy sufficiently more or buy at sufficiently higher prices such that credit card transaction costs are more than offset.
That is the only reason why a cash/debit card discount would not be advertised.
Edit to respond to below:
I don’t buy that. Merchants of all types already engage in myriad types of discounts and promotions to price discriminate customers all the time.
A simple sign saying “x% discount for paying cash/debit” is of negligible complexity.