Debit cards can do the same job for basically no fee.
Credit card users, however, are likelier to spend more money, and that is why many retailers are hesitant to charge credit card users more than debit card users.
Edit: note that Target does give a 5% discount on everything you buy if you pay with your bank account tied to their debit Red Card, so some retailers do seem to be changing ways.
I’m not sure which debit cards you’re referring to (e.g. Interac vs VISA debit) but AFAIK they all have fees, with possibly different structures, e.g. a fixed charge + lower percentage.
Credit card users, however, are likelier to spend more money, and that is why many retailers are hesitant to charge credit card users more than debit card users.
Edit: note that Target does give a 5% discount on everything you buy if you pay with your bank account tied to their debit Red Card, so some retailers do seem to be changing ways.