EU only capped fees for 4 party systems, and only for consumer credit cards. business credit cards and 3 party systems (American Express for example) are not part of the cap and you can get more rewards with these card types.
Quite a few places do not accept Amex and many that do probably don't know they do or they would disable it.
Quite a few places do not accept Amex and many that do probably don't know they do or they would disable it.