The issue with your solution still comes down to yet another centralizing middleman with no real incentive to be efficient. And all the incentive to lobby governments and extract more wealth from the people.
This can of course be done government by government, but that isn't scalable for a global company.
the middlemen aren't intercompatible. it's like saying anyone can make paypal.
If you try to start your own paypal, no vendors will sign up because you have no clients. No clients will sign up because you have no vendors.
My university forced everyone to use duo mobile for years, with no other option for OTP. That's what this reminds me of. Sure, there is a sense in which the university can choose to use a different 2fa service, but there is nothing forcing them and the consequences are on the user side.
There are multiple credit card companies. They try to attract customers and merchants with promotions and lower fees. Even Paypal has competition.
Companies have cracked the problem of signing up clients and vendors simultaneously in other sectors of the internet economy. This is an annually recurring revenue stream that virtually every adult will spend money on. I'm not super concerned about competition, as long as anti-trust enforcement remains strong.
This can of course be done government by government, but that isn't scalable for a global company.