Not exactly what the OP is talking about, but I do consulting and have ~5 gmail accounts.
My FAVORITE feature ever is: "huh. You just woke up on a Tuesday and need to get to work? Well, we've logged you out of all your accounts and need you to log in again."
My FAVORITE feature ever is: "huh. You just woke up on a Tuesday and need to get to work? Well, we've logged you out of all your accounts and need you to log in again."
The worst.