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.