Where do you think those fees come from? You! Rebates are your own money you have to optimize to get back, and those who are less well off are usually the ones who are disproportionally impacted by the aggregate costs of reward cards (because they're paying with cash, debit cards, or other mechanisms where they don't receive a rebate).
Rewards for payments and unregulated interchange fees need to die. They are a financial transaction tax on everyone.
No, they are partially a cut of the fees the CC company charges. Show me proof that they're 100% from fees and I'll believe you. Otherwise a quick google search shows that you're not correct here.