I think AMEX able to have higher fee because they're underdog in that market. For the same reason a lot of places in EU / UK dont like to take AMEX.

Amex get away with it because their customer base is a niche of higher income earners. Merchants would rather not accept Amex, but a lot of them want to attract that demographic as their customers. So they each make their own decision about how to balance those concerns.

Of course, the value of the system is that it's a global payment network. If the card brands started cutting out over regulated markets then the system would decrease in value for customers in it's main profit centres. The outcome is just that the rest of the world ends up subsiding European payment networks. The negative impact of policies like this isn't that the payment networks will start exiting markets, it's that they just won't innovate. Which is why most of the innovation in the payment industry recently has been in EMIs and in-app payment systems, which are both more expensive and worse for consumers.

But all of this is secondary to the point, which is your claim that a 3% processing fee is insane. The way the system works is insane, if you said today that you wanted to build the type of system that the card bands have built, nobody would believe that it would be possible. Especially not all for a 3% processing fee. If the payment networks didn't exist, everything you buy would be a lot more than 3% more expensive, and your quality of life would be very notably reduced. The value you're getting from them is a lot more than what you're paying to use them.

That’s largely because the widely-reported 0.3% are the issuer’s takeaway, while the 3.5% are the (average? maximum?) cost to the merchant, so it’s not even an apples to apples comparison.

Out of the latter, three parties are paid: The issuer, the merchant acquirer, and the network.

Merchants pay significantly more than 0.3% to accept card payments even in Europe.

That said, US interchange rates (i.e. what the issuer gets) are much higher than 0.3%, which is why there’s credit card rewards.