Merchants absolutely can pass on the fees or give "discounts" for cash, at least in the USA. Gas stations are one of the major businesses that practice this.

Anecdotally, I worked at a company store years ago where we would charge customers paying with cards a 2.75% fee, which is what we were paying. And that store was operated by a Fortune 500 company.

Also, virtually every small private business I go to in Los Angeles charges some fee, or has stipulations, for credit card transactions.