I visit a number of various businesses that do not accept American Express because the fee that business is charged for allowing people to use an Amex is higher than the fee they are charged when their customers/clients use a Visa, MasterCard, etc.
But I recently learned that Square, a company that processes credit/charge card payments charges the same clearing fee whether the payer uses an Amex or a Visa/MasterCard, etc.
For all payments, the fee is 2.75% no matter what type of card is used. Maybe more businesses will start to accept Amex. I hope so!