Why do you say they cause higher prices for rewards recipients? Is there evidence of this?
Many rewards programs are also predatory in the way they want to sell your data so you are targeted by advertisers for products you wouldn't buy otherwise.
Granted, some slice of it is kept by the issuers, but it turns out issuers mostly make money on interest not interchange.[1]
[1] https://www.valuepenguin.com/how-do-credit-card-companies-ma...
Meanwhile in Europe the issuers are capable of running a profitable business on only 0.3% fees (and much lower for debit). So even though you may think rewards programs are nice, they are in the end costing you more, not giving you free money.