Interestingly a barber in the City (of London) I occasionally go to started accepting Amex recently. I had asked them the first time I used them (back in 2008) why they didn't accept Amex and it was for the high rates.

When I asked why they'd started accepting Amex, they said that the rates on some rewards cards they were accepting were so high that Amex was better value for them.

I also assume it was helped that the demand for Amex is higher in the City than the UK average.