Not anymore, have you been in Europe in the last 3 years? Amex tried hard to get more acceptance in Europe, for once lower the merchant fees and try to push out cards with nice benefits like the SAS Amex.

I travel on business all over Europe more or less on a weekly basis I usually get along fine with Amex. I would say almost all hotels take Amex and in shops, restaurants, taxis, etc the chance they will accept it is quite good.

Of course it is wise to carry a MasterCard, Visa or even Maestro (for Germany and Austria) as fallback.

Actually, I think I managed to live largely without cash for the last years which was not possible years ago.