Unless you work on a public computer, and you don't want some random person to stumble accross your 3DS account and post something violating the TOS. I dont' have this problem, but others might.
I don't have to log out? It's got something to do with the cookies, I guess. But I'm using three different browsers, does that affect it? Like, I log out using Net+ and login with Netscape? Will something be lost?