Because the rewards are, from your perspective, a discount on purchases you would have made anyway, since most merchants charge the same price for both cash and credit card transactions. (There are costs associated with handling cash that, depending on the business, can end up being as expensive as paying the merchant fees to credit card companies—accepting credit card payments is not just a pure convenience to the customer.)
And they probably administer rewards programs for banks and various other organizations that want you to use the credit card they issue instead of the credit card issued by some other bank.
Because the rewards are, from your perspective, a discount on purchases you would have made anyway, since most merchants charge the same price for both cash and credit card transactions. (There are costs associated with handling cash that, depending on the business, can end up being as expensive as paying the merchant fees to credit card companies—accepting credit card payments is not just a pure convenience to the customer.)
And they probably administer rewards programs for banks and various other organizations that want you to use the credit card they issue instead of the credit card issued by some other bank.