That would not work for a number of reasons, the first one being the fact that virtually every service now uses HttpOnly cookies for session management (to make

That would not work for a number of reasons, the first one being the fact that virtually every service now uses HttpOnly cookies for session management (to make it harder for e.g. XSS injected code to steal sessions). In addition to that session cookies are usually rotated very frequently, with servers occasionally updating them even if you stay logged in; it goes without saying that if you log out and back in you will almost surely get a different session token each time.