You cannot change the URL like that. URL need to be in same origin as the current URL to be changed.
https://accounts.google.com/reallyuglyurl?lotsofvars=true&XSS=here
once that hypothetical XSS is discovered, then the attacker can pushstate the page with the XSS to look like the login page...Personally, I'd rather take actions that don't require user interaction, like stealing the user's session cookie silently in the background or making other requests on their behalf to the website. That can be done via an invisible iframe on an otherwise legitimate website (which, I suppose, you could also consider to be "dangerous").