It saves one click if I just sign in and am going somewhere.
But if I selected my destination at first (instead of Sign In), and then was sent to sign in, there is no need for it to pop up again. In this case, it is a nuisance and causes an extra click (somewhere else on the page) to get rid of it.
And if I click on the wrong place on the page to get rid of the drop down menu, I go somewhere else I did not intend to go, and have to click my way back to where I wanted to land in the first place. And usually the back button does not take me where I came from, so then I wind up starting over at the home page and drilling down again.