Agreed, I make almost all my purchases with my Amex card (mostly because of unlimited 2% cash back on everything). It's usually smaller independent restaurants that don't take American Express. It's something that I never really understood, because American Express in my experience charges lower transaction fees than Visa/Mastercard. When I had an Amex merchant account they charged a flat $7/month fee with no per-transaction fees, though our volume wasn't very high.

However, you have to setup the American Express account separately, which probably has a lot to do with why many mom and pop type restaurants don't take it. But now that a lot of new restaurants seem to be using processors like Square, this is a complete non-issue.