Not sure what browsers allow, but, for example, you could manage auth/sessions for homeservers, you could offer to server Pubky profile/web pages that render from keys, you could integrate pkdns and serve dns for keys, allow people to render web pages from key domains, parse key domains into nicknames on the page and/or browser bar, etc etc :) 

 I just wish it were possible to access a website using the public key as the address, serving files directly from your home server. 

 You could do this by running pkdns locally, then pointing your browser DNS to it. 

 I think a browser extension could simplify this process. That's the point.