At least in the UK, merchants pay very low fees to process debit card payments, to the extent that some merchants (e.g. budget airlines) do not accept or charge a penalty for using credit cards.
Merchants pay up to 1.75% (Square) to process in-person payments. Whether this cost is embedded into the prices of what you buy or whether it's made clear to you is irrelevant to that point - that you're paying this. And even when credit cards are more expensive to process - do you ever get a discount for using a debit card at the supermarket? Cash?