My years in fintech have taught me that it'll be very difficult to get these charges down without legislation. What they are is, essentially, insurance.
For Visa/MC, "running the network" at cost is possible on much less money, but the network involves a lot of elements along the chain that can get transactions reverted. The "insurance" (1-3% of tx) pays for the legal-adjacent issues related to handling those transactions being contested.
Go to a restaurant, use a US terminal? Great, the restaurant owner can modify the transactions after it's been authorized and long after you're gone, "because tip". There's zero checks on this, it's a matter of "it works because most people don't do it". So when it happens, sometimes the payer notices and issues a dispute and the dispute management is part of the network. This is where a lot of costs go.
Anyway, the network is ridiculously bad. The fraud/aml checks are not usually shared among payment providers, because they can just milk each other instead by selling their checks. No wonder it's hard to get the transaction fees down.
And yeah, it's a duopoly. The solution by the way isn't to directly try to build a global visa/mc competitor; with the moat, that's impossible.
Rather, it's to build on top of what European countries are doing. EU countries have built their local competitors (Bancontact, EPS, BLIK, iDEAL, Sofort, ...). Those have lower costs, and so would any locally-targeted provider because they each have to deal with less risk and complexity. Any aggregator (like Stripe is, by the way) can take payments for all of them and push people away from card payments. The problem with that very last part is a UX issue, people like paying by card.
It's a difficult problem. What makes it especially difficult IMO is that once you're down this path and become successful, it takes some very specific, very early business choices in order to be able to turn down the mountains of cash that show up to your doorstep in the form of "align your fees with the rest of the industry".