There are other considerations that need to be fixed first. Fraud protection has historically been stronger for credit cards than other means of payment in the US. Likewise cash back vs not.
Fraud protection is inherently better for credit cards, because you haven't spent your money. The bank has spent the money, and you don't have to pay the bank if someone defrauded the bank. So the bank has every incentive to get the money back. Not so with debit. You spent your own money.
That cash back is basically a scam. It's paid for by the credit card processing fees - fees which are charged to merchants and ultimately get passed on to the customer in the form of higher prices. Some merchants even tack on explicit ~$3 transaction fee for credit card purchases, to cover transaction costs.
So the cash back is just a partial refund on your credit card processing fees.