what's the point of having them? inarguably just wastes time. it should just take you straight in or straight out. if it fails, then it fails; let the user know. but i'll know if it's successful or not depending on whether my name is at the top right
If I make a typo while writing my login info and don't realize it, then I might not realize (right away) that it didn't work because I don't instinctively look for my username in the top-right corner every single time I log in. Maybe you do, but I don't think it's fair to assume that everyone does.
In my day, I've witnessed a plethora of websites that just throw you back to the main page when you get your login wrong, and I've even seen some small sites so broken that the page would be reset even if you got your login right, without any error message explaining what happened. I honestly believe that the extra confirmation is helpful.
I suppose this argument is less applicable to when you're logging out, but I imagine it probably serves a similar purpose. I don't see any reason to NOT have either screen, anyway.
In my opinion, all of the "wait to get redirected" screens are needlessly time-consuming and could easily be replaced with a message at the top of the page. I've experimented with it in the past, but I couldn't come up with a design that looks decent on all site schemes.