Neither Citi nor Capital One entertain "I made this charge but I don't want to pay it because I'm angry at the merchant for bad service" (or whatever) easily. At minimum you have to prove that you tried to remedy the problem with the merchant and they're refusing.
One silly example that happened to me. I bought a dishwasher and it had a problem. Under EU law, the retailer covers the warranty the first year and then the manufacturer warranty kicks in for years 2 and 3. Under the manufacturer's warranty they would dispatch a technician to my home. But the for the first year I would have to carry this big bulky appliance back to the store for them to look at and repair it.
In the end I sat on the problem for a few months until the "real" warranty kicked in and had a technician come out.
I don't think this was intentional but an oversight in the original consumer protection law.
http://europa.eu/youreurope/citizens/consumers/shopping/guar...
Thus, local legislation in an EU country may give better protection; for instance, here (Finland) there is an additional defect liability which says that if an item is supposed to last longer than 2 years (e.g. a dishwasher), then the liability "wears out" over the reasonably expectable lifetime of product. You won't get a refund if a 6 year old washing machine breaks (yes, I won't buy another LG), but you can get a partial refund if a 3 year old machine breaks down.
This liability falls on the retailer; importer/manufacturer has only secondary liability.
That's one reason some stores(like Winco) only accept debit cards: The processing fees are much cheaper. And it might be because they don't have to enforce chargebacks, by law.
Certainly it's possible to accept payments with low costs: Bank transfers are pretty cheap.