So you hate getting something back for choosing one payment method over another when there's no indication that retail stores would lower their prices if credit cards (and their transaction fees) were wiped out?
Competition will lead to that. It doesn't happen immediately, it happens in waves. These are called price wars. When that happens, they try to undercut competition at every possible turn, and having lower payment processing fees allows them to go lower. Who wins a price war? The consumer.
Yes: points are ridiculous. The fact that credit card fees are passed on to cash payers is ridiculous. Visa and Mastercard are absolutely minted. Where does that money come from? You and I.
(and: why does competition not work for Visa and Mastercard as well as it does for retailers? Because the feedback loop is much longer. Intractable, in practice. Choosing one retailer or the other is a clear signal we can send. But are we going to choose merchants based on payment processor support? As for merchants, they're stuck in an oligopoly. Competition is gone, leading to this unhealthy market.)
They are probably illegal (or against contracts) in most states, but you see them very often.
Minimum purchase requirements for credit cards were explicitly legalized in the US in 2010 as part of Dodd-Frank. Merchant agreements are not legally allowed to prohibit them.
"2010 law: up to $10 minimum OK. The law says that merchants can set a credit card minimum purchase of up to $10, as long as they treat all cards the same. It also allows the Federal Reserve to review and increase the minimum payment amount."