Payment processing costs are a scam. They're 10x as expensive as they need to be to fund rewards programs and fund the financial system.

EU max credit card transaction fees are 0.3%, in the US they can be up to 4%.

It just doesn't cost 4% of a transaction to handle the exchange of funds. Just wealth transfer to finance people and the upper class who take advantage of credit card perks.

Can someone explain to me if EU card transactions are capped, why Stripe charges me (US) the full ride on my EU customer's cards? In fact, I get charged even more for EU cards – perhaps as much as 2.5% extra.

I just checked and I get charged ~8% in fees on a 10 euro transaction on Stripe. Of course some of that is the low transaction amount (flat 0.30), but it's brutal for a small business like myself.

    2.9% + 1.5% (intl card) + 1% (currency conversion) + 0.30

    Payment amount (€1.00 EUR = $1.15253 USD)
 
    €10.00 EUR -> $11.53 USD

    Fees

    Total:    - $0.93 USD

    Stripe currency conversion fee 
    - $0.12 USD

    Stripe processing fees
    - $0.81 USD

    Net amount
    $10.60 USD

As someone who really enjoys rewards programs, keep those scams alive!

Except in the US, it does. Depending on the card, it can cost as much as 4.5% (or more!) to run the card. You can argue that it shouldn't, but that's a different statement than it doesn't.