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Additionally, Amex provides both the credit as well as credit card processing for their customers instead of splitting the business with thousands of banks. So when a merchant exceeds whatever shadiness threshold is set by Amex they are banned from accepting all Amex cards vs. cards issued by $yourbank. So there is incentive for the merchant provide good customer service.

Re: shortstuffsushi

Generally, merchants don't take AMEX because it's expensive to do so. The fee rates are usually higher (~3.5% vs ~2.5% and there is a monthly access fee as well.

Is this a reason that many merchants don't accept AmEx?

Partially, yes. But Amex also charges higher transaction fees, which come out of the merchant's profits. Between the two, and the fact that only ~20% of people have an Amex, many merchants decide Amex isn't worth the trouble.