No. I've got Firefox configured to nuke almost everything on restart, plus I run PrivacyBadger and uBlock Origin. This is not me overlooking an existing login.
(I also run a site-specific browsers via Chrome to isolate my Gmail login and keep Google from knowing who I am, I have no Facebook login, etc. I'm not serious enough to run a VPN or Tor, and my setup isn't enough to guard against browser fingerprinting, but I'm reasonably paranoid.)