Much of that goes back to cardholders in the form of cash backs. That is evidently friction not necessary to run the system.
The 3.5% get split among issuer (how much they get is public information), network, and acquirer. We also know how much issuers roughly pay out to cardholders as cashback/rewards.
The EU took that information and acted on it by outright capping the issuer portion (i.e. the interchange).
One half of the US approach for debit was similar – Durbin capped debit interchange to an extremely low percentage – but the proposals from this (now rejected) settlement look different and more market-based in that they'd allow merchants to effectively collect back the cardholder cashback in surcharges.
Durbin also has a less-known component of trying to create competition between networks by mandating debit cards to have two independent networks. Extending this to credit cards could possibly help drive down actual network fees, but this has arguably not even worked that well for debit. Also, as many people have mentioned before, the interchange slice of the swipe fee cake is by far the largest and would probably make more sense to tackle first.
The outcome of this sort of regulation is that nobody wants to invest in establishing or innovating large networks like this. Which is why all the recent innovation in payments has been centred around terrible, highly fragmented, in-app payments and EMIs, and that’s certainly not a win for consumers.
That's certainly much more than just the cost of running the technical network, but also, as we can see from the above calculation, clearly one of the smaller components of the 3.5% (since the lion's share goes to the issuers).
In that sense, the networks really do compete – for the issuers' business! Issuers then compete with each other for cardholders by paying out cashbacks, but what many find missing is competition with these dynamics as a whole.
Making that cost explicit in the form of credit card surcharges might have been a path there (I'm not sure if I'd have been a fan myself), but since this settlement is now off the table, let's see what the next move is.
And yet, fees are 0.3% in Europe, and VISA, Mastercard and Amex are still happy to do business here. And customers can STILL pay with a single FaceID with Apple Pay.
So maybe all 0.3% of trillions of Euros moved is still enough to do all this.
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.
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.
The payment card system is a miracle of system design and global commerce. I also want to see processing costs come down over time, but 3% is a bargain for the value you’re getting, and if you wanted to stifle any further innovation out of the industry, then regulating the profit out of it would be a good start.