On fees, it's typically just the network fee (e.g., Mastercard) that gets waived. The issuing bank, acquiring bank and the processor, still take a cut.
Bank transfers have too much friction. You wouldn't pay your corner store with a bank transfer. You'd rather swipe a card. It's why you carry around your bank card (which as a VISA or MC logo). You wouldn't pay for something on eBay with a bank transfer. You'd use PayPal. An interesting point is that both PayPal, VISA and Mastercard on the bank-end are really just a series of bank transfers wrapped with a more refined consumer/merchant interface (card / POS terminal).