> If some site has an XSS vulnerability, then they've already got access to my session cookies
Not true if the website uses HttpOnly session cookies as they should.
Not true if the website uses HttpOnly session cookies as they should.
They can also set up a keylogger or fake login screen and wait for you to type or paste in your password yourself.
I've always thought HttpOnly cookie flag is overrated. Stealing the session cookie may be the easiest attack but it's hardly the only.