When I ran a retail shop in the US I never accepted AMEX because the fees were significantly higher, mostly because of the flat monthly fee and low volume of people using AMEX.
Frankly I don't know how they are still around. Since everyone with AMEX always has a back-up card there is no incentive at all for merchants to accept it.
The original way they did things was by being available only to rich people and then trying to get merchants to treat them extra nice. These days they charge merchants and bribe consumers with extra goodies. If you're into points or miles, you can usually get more on Amex or Diners.
Frankly I don't know how they are still around. Since everyone with AMEX always has a back-up card there is no incentive at all for merchants to accept it.