The EU has been moving in this direction with PSD2 and it’s been pretty good. Downside is there’s no defacto standard for APIs and each bank's development skills vary widely.
PSD2 is really bad. It doesn't actually allow you, the customer, to sign in to your banking account using your own application and an API.
It only mandates that regulated thirdparty companies can access your banking account using some API.
Here in Germany PSD2 was a big step back. Previously we had FinTS (https://en.wikipedia.org/wiki/FinTS), an open banking protocol used since the last 90s, and many programs supporting it. Then PSD2 came and broke some use cases of FinTS. Many banks didn't want to both fix FinTS and support new PSD2 APIs, so they just switched off FinTS. Now German bank customers are basically forced to use the banking website because PSD2 doesn't allow them to use an API and the API they had was taken from them by PSD2.
From what I remember FinTS was a very escoteric protocol and super low level. What PSD2 promises is modern APIs that devs from this millennia are used to to build off of.
It's true that the 6,000 banks in Europe have different standards, but the fact that the APIs exist and work and that the regulator is enforcing the use of real APIs (as opposed to screen scraping) is worth the effort to integrate each of the banks.
I work at Nordigen and we integrated with 1,500+ banks in less than 8 months. Some APIs took hours to integrate, some took a few weeks, but the fact that it was possible at all is IMO gamechanging.
The great think about PSD2 is that it comes with a bunch of laws and regulators are generally good at making banks compliant. An API that's not working is a non-compliant API and banks get it. PSD2 came in to force in Sept, 2019 and 2 years later all the major retail banks in all EEA countries work have fully operational APIs.
One major limitation is that PSD2 only regulates access to payment accounts, but doesn't mandate access to credit cards, investment accounts, savings accounts etc. This is why screen scraping (to everyone's dismay) is still used - to "expand" what's possible with real bank APIs.
