Federated logins are a thing! The challenge is finding one that's open and privacy-friendly. Unfortunately the widest-used ones come from entities like Google or Facebook with a marked interest in preying on user data. Mozilla used to maintain a federated system (Persona) but they discontinued it. I know Ubuntu offers one for all their services (bug trackers, forums etc.) but not sure if it's open to third party systems. Perhaps there are others worth using.

Alternatively, you can aggregate all your logins in one place across devices and browsers. Firefox Accounts are a very simple method of doing this (presuming you use Firefox everywhere), and you can choose to only sync logins rather than bookmarks, plugins etc. And of course there are other dedicated password managers, with or without online sync, open or closed source, self-hosted or private hosted etc.