OpenID does exactly that and has been a thing for something like 15 years now.
Quite a few big sites like Yahoo, Google, AOL Verisign would provide a URL you could login with (they were identity providers) and there were lots of independent providers too. You could easily host your own with as simple PHP script.
Sadly, fewer large sites would actually accept OpenID as a way of logging in, but you could used OpenID for authenticating Blogger comments. Stackexchange supported OpenID logins for 8 years [until July 2018](https://meta.stackexchange.com/questions/307647/support-for-...).
Quite a few big sites like Yahoo, Google, AOL Verisign would provide a URL you could login with (they were identity providers) and there were lots of independent providers too. You could easily host your own with as simple PHP script.
Sadly, fewer large sites would actually accept OpenID as a way of logging in, but you could used OpenID for authenticating Blogger comments. Stackexchange supported OpenID logins for 8 years [until July 2018](https://meta.stackexchange.com/questions/307647/support-for-...).
The BBC wrote quite a good summary of how things stood in 2008: https://www.bbc.co.uk/blogs/bbcinternet/2008/10/openid_found...
It's another one of those sad parts of the web we lost.