Is there some shortcut I'm unaware of? Because I can't see much difference between [starting paint, resizing the default canvas to something smaller than your screenshot if necessary, hitting ctrl-v, ctrl-s] and [starting paint.net, hitting ctrl-alt-v, ctrl-s]. Personally, I think that not having to consider the size of the image to be pasted saves more time than waiting a little longer for the program to open.

On the other hand, I see that Paint actually does support PNG now, so it's worked its way back up to cutting-edge 1996 technology.