The account ids are all different, aren't they ? And they are not related. Even if one account gets hacked, it won't give a clue to what my other accounts with other brokers are. The account ids are only stored in my head.
My passwords are generally secure. I have an idea about the password strength. In my computers, the C drive is frozen (the variable data is stored on the other drives), so whatever cookies are stored during the session are wiped clean on reboot. I only unlock it 2-3 times a week for various software updates (antivirus, flash etc.etc..)
As for saving passwords online.. suppose that password storage gets hacked ? Not good to put all your eggs in one basket. Recently there have been a spate of cases of so many million google and apple ids and yahoo passwords being hacked and some of them even displayed in public domain.