Yes, because forcing me to carry cash around is a real protection of my rights as a consumer. Thanks for being my champion.
Visa's policies are for their own benefit. Coincidentally this policy might help consumers like yourself who don't prefer carrying cash, however that's not visa's primary intent... they benefit greatly from forcing stores to run inexpensive purchases.
I just spoke with my father to find out how this all works. Admittedly our store is not typical and this might be different for other stores, especially larger ones who can negotiate with visa.
In our case we pay a flat percentage on every purchase regardless of cost. So hypothetically given a 1% rate a $5.00 purchase might cost us $.05 and a $500 purchase would cost $5.00. That makes sense, and if that was all that mattered we'd be happy to accept cheaper purchases.
Unfortunately that hypothetical 1% rate isn't set in stone. It's based on the average transaction amount... the lower the average transaction amount (i.e. more $5.00 purchases) the higher the rate. If you only sell cheap things, and most of your purchases are going to be small that's fine... you can compensate by raising prices a small amount.
In our store (and probably in some of the other stores that have similar policies) the average transaction rate is relatively constant but the minimum and maximum transactions differ significantly; one sale may be a greeting card for $2.25 and the next might be lighting for $6000.
If we were to allow people buying a single greeting card for $2.25 to use their card our average transaction rate would drop significantly and the flat rate we pay would go up. We could compensate by charging $2.40 for the card. That would be enough to cover the difference. We can't however charge $7000 for the lighting... small transactions can result in very large costs for larger purchases.
Basically we'd be fine if all we did was run $5.00 or $10.00 transactions. Then we could just raise prices a little bit... in our store we can't do that though. Raising the cost of a card by 5% will not cover the lost revenue from the lighting sale.
Does that make sense? If visa really cared about consumer rights they wouldn't penalize stores so much for cheaper transactions, or, like a debit card, they could charge a flat rate for larger purchases. For example, if you were to pay for that hypothetical $6000 lighting purchase with your visa it might cost our store around $300 to run your card... but use your debit card, and it costs us around a dollar.