US banks have something mostly like this: Zelle [1]; the company behind it, Early Warning Systems, is owned by JPMorgan Chase, Bank of America, Capital One, Wells Fargo, PNC, basically every bank has a stake in it, and every bank supports it. And it works better than Cash App/Venmo; enter phone number or email address, get an instant direct bank-to-bank transfer, no fees, all from the normal bank app you'd already be using.
What we're really talking about with FedNow is not user-facing: Zelle runs on Mastercard Send/Visa Direct, but traditional bank transfers run on ACH, which is very antiquated. FedNow is supposed to replace all of this (though, who's to say if Zelle would actually use it; its possible Visa/Mastercard have stakes in it as well, and they'd lobby against it; but, even in those cases, Visa/Mastercard likely make heavy use of ACH somewhere, and they'd be using FedNow. Its all ACH all the way down)
Zelle's issue is really that most people don't know they have it. For example, Chase has had, for a very long time, QuickPay, which could be used to instantly send money to other Chase customers. Naturally, no one relied on it very often, because if I'm out for drinks with my friends, I'm not going to lead with "Hey, do you have Chase?". QuickPay now uses Zelle, so the bank doesn't matter, but people have their apps.
Its actually the exact same "problem" as WhatsApp is elsewhere in the world. Upgrades to the fundamental, platform-agnostic technologies (SMS->RCS, ACH->Zelle->FedNow) lose stickiness when people have "their app" they'd rather use. In my view, Zelle is one of the greatest tragedies in the US financial system; the banks did everything right with it, its an incredible product, but even very smart people I know refuse to use it, because its not Cash App or whatever.
[1] https://www.zellepay.com/