This would require either a central authority for registering and managing the identities, or the path of distributed ledger, where identity is confirmed with digital signatures when transacting - the second option is what crypto is. Some type of Blockchain tech could service it but all crypto related technology is buried in bad optics right now due to the current state of it being a big mouse trap setup by venture capital to squeeze money out of people without the protections of regulation afforded by their centralized identity management (which is run by the native government that the users are a citizen of.)
That then introduces ease of use problems. You won't be able to log in to another device without copying your key over from an already logged in device for example.
Web browsers don't usually allow access to local files made outside the browser, so even logging in between browsers would require having your key on hand.
Not to mention if you lose the file containing your key (hard drive craps out, etc), you'll lose access to your account entirely. So users would be forced to backup their keys.
Not issues that would make the product unusable, but enough of a hindrence that 90% of users would just go find something else (like threads) to use instead.
I can't use my account on another device until I input my password, so either way I need to use a password manager. If you reuse the same password (so you can remember it for hundreds of sites instead of using a password manager), being forced into using a key instead would actually be an improvement for your security.