“...Merchants will never reduce prices of their products, you can bet on that.”
It really depends on the Merchant. In the smaller, brick and mortar stores, where you may sometimes deal with the owner, or an owner informed associate, you can get a discount by paying cash. You just have to ask at check out time. I have done this many times locally or as a tourist.
We have been using credit cards wherever and whenever they are allowed - thanks to credit card points, we brought the grandkids to Disney and we get the bulk of our Christmas gifts. I figure the cost of credit cards is already built in to the prices merchants charge. That said, if the discount for cash is a better deal than credit card points, then we'll be switching back to cash.