Rewards are hoops CC card companies make you jump though to get some of your money back. Money you pay when vendors increase their prices to cover CC card fees.
Pedant rant/ That's not quite how pricing works. Firms will generally charge the highest price the market will bear. If the firm is already charging that price, demand decreases if the raise the price. Depending upon the price elasticity of demand, it may be a precipitous drop. The firm is more likely to just have diminished margins.
I don't know what credit card you have experienced this with, but with mine I just indicate that I want cash back in the form of statement credit and it's good to go. There are no hoops to jump through.