Piranha: Right, I understood that you weren't suggesting that the user should login with every click.
I was saying that by using a cookie solution where every new login has the effect of logging out every other session of that same username, you create a situation where it becomes impossible for two (or more) people to use the same userid because everytime of of them logs in, they log the other person out.
For example, user A buys a subscription to your web site and shares his userid with user B - or maybe posts his username/pass on some web site for lots of people to share. User A logs in, starts doing stuff, and then user B logs in on a different machine. Now when user A tries to do anything, he's been logged out by user B so he has to login again - which logs out user B. So it becomes frustrating, or even impossible, for two (or more) users to share a single login.