Logging out of the stack exchange sites is a bit of a formality for me. I only log in from the one PC which no-one else has access to. I'm aware that there are ways that people could impersonate me if they really wanted to, but the security level is plenty enough given that no-one would want to.
But I still find it odd that it's increasingly difficult to log out and stay logged out. I'm surprised that anyone who shares a PC, or who's main PC is easily accessible by others, isn't complaining.
Basically, I make a point of doing the "Log Out Everywhere" when I log out of the last stack exchange site - and of then stepping through them to make sure they're logged out. Not from paranoia, but through curiosity - I've always had a certain rate of finding myself logged in when I'm convinced I logged out.
Yet when I return, so long as it's some time later, I always get the "Welcome back" automatic login without my openID or password being requested - at least I have since this new feature was added.
An additional issue - it seems impossible to be logged into one stack exchange site, but to view another (perhaps accidentally due to Googling) without getting logged in, irrespective of whether I want to be logged in to the other site.
My browser is set not to store passwords for anything, so nothing is using that. Quite simply, if someone had access to my PC, they'd only have to select a bookmark to access e.g. Stack Overflow, be logged in as me, and to be able to impersonate me.
What's going on with that?