The U.S. has a real-time payments system. (One of the oldest in the world.) It's called Fedwire [1].
It's artificially kneecapped–Congress set a minimum fee of pennies on the dollar and many banks charge retail clients $10 to 35 for wires. But the rails are there and used and understood.
(Detour: my "abolish the penny" issue is expand Fedwire's market hours, enable it on weekends and remove all Fed fees for wires under $250,000.)
[1] https://www.federalreserve.gov/paymentsystems/fedfunds_about...
That is almost entirely your bank charging a mark-up.
The Fed charges its members between 3.3¢ and 84¢ per wire, depending on things [1]. (It can go as high as $1.20 for a $100+ million wire from a bank that handles fewer than 14,000 wires a month.)
My bank, for instance, doesn’t charge anything for wires.
[1] https://www.federalreserve.gov/newsevents/pressreleases/file... page 34