Why? If the merchant is paying an extra 1-2% for your purchase in cc transaction fees, why should they be expected to eat the cost? Why should your service be subsidized by people whose transactions don't have that overhead?
They are paying even more to manage cash but don’t have a separate fee for it. Why should credit card users subsidize that?
(Personally I think it’s fine to charge any which way you want as long as your terms are clear. But I think this answer makes clear it’s not so obvious as you suggest?)