I have Firefox set to not remember history and clear all cookies, caches, etc. after quitting. Then if I am logged into two sites at once for some reason, I won't forget to log out of each. Quitting Firefox will clear everything.
You are dealing with the vulnerability of someone logging into or having physical access to your computer. The logout and close browser routine is intended to shortstop a vulnerability that arises from a hacker actually hijacking your logon session —
while it is in progress. In this case clearing the history etc. is a case of
locking the barn door after the horse is long gone.
