I doubt they care, as their business is built on quality, not quantity.
Average Amex cardholder already charged to their card roughly 10x of what the average non-amex cardholder charges.
HaHa, yup, but it seems they're fat & happy where they are, with high fees on both sides. Their services are so much better than V/Mc that they could rapidly swamp V/Mc, IFF they'd reduce their fees. But they are obviously not interested in any other than the market segments they've got.
AMEX won't lower their surcharge. Until they do, they will always lose business to Visa and Mastercard.
It's pretty rare that my AMEX card gets refused...
Might depend on the country. It happens a fair bit down in Australia
Maybe USA-specific, but I've been AMEX-only for around 20 years, and have no regrets. They handle fraud and chargebacks with almost no effort or followup required. Very infrequently, I'll run into a cheap-ass merchant who doesn't take AMEX, and I will either not do business with them or just pay in cash.
Yeah, AMEX has lots of issues getting accepted outside the US. Some places won't accept tap-to-pay for Amex, but only chip+pin, or various other oddities, if they accept it at all.