I once had a conversation with a merchant about not taking AmEx. He told me they could take it, their machine and merchant accounts were all set up, but instead of getting paid [whatever they charged] - [small percentage merchant fee] relatively quickly, they were sent a bill for AmEx fees that was almost impossible to correlate with sales. AmEx only paid them for the sales later.

AmEx are 'better' for customers because they screw the merchants over.

In my experience any time a merchant tells me they don't take Amex, they actually do take Amex but the owner / manager doesn't like paying the higher merchant fees so refuses it since most people carry an alternative payment card. I generally insist, and actually if any merchant /does/ accept Amex and claims they don't, it's a violation of their merchant agreement and you can report them for this.

With the exception of international travel, while I'm in the US I generally /only/ carry my Amex, because it's as good as cash for any of the businesses I'd generally want to frequent anyhow.