Why hasn't such standardization happened?
Browsers may just be a relatively transparent means to an end, especially in the app world. The differences between them are small, to the average consumer, and I'm guessing whatever is solved by moving them to the browser is trumped by the existing state, syndicating the credentials you already have with the companies you trust, saving credentials to the browser and easy to remember (insecure) passwords.
https://en.wikipedia.org/wiki/Mozilla_Persona was great. But, what customer problem are you trying to solve?
Because everyone has their own vision of what should be a "standard".
- That's why you still have browsers that don't render the same way.
- That's why you have 100 JS frameworks that try to push their way of doing things.
- That's why you have 50 CSS pre-processors.
- ...
Think of the number of times your computer has crashed, had memory wiped, new OS installs, been stolen, replaced. Did your bookmarks from 15 years ago survive?
With mobile phones identity works a little better and likely because of SIM cards.