Credit card rewards are not a mechanism to shift wealth towards premium card holders (this is a negligible distraction), they exist purely to increase revenue/conversion rate, by decreasing customer price sensitivity (compared to cash payments) and encouraging financially irresponsible spending. If this did not actually work in practice, every merchant would just insist on cash and pocket the difference.
"Poor people" are hurt much more from the changes in spending behavior induced by credit card use than by paying for card rewards.