[whpalmer4]

The Inspector window is the only "utility" window that it restores on launch; Attachments, Preferences, Release Notes, Perspectives, Help windows are not restored. I suspect they view this as doing you a favor and starting you off with an uncluttered workspace. They do record the position and size of the window so that it goes back exactly where you had it when you recreate it.

Are you using the window all the time for launching perspectives? Even with a 27" display, I find that window takes up too much space to leave up. command-control-P is my friend, maybe it can be your friend too :-) I think it is about the only window that opens quickly for me!

Perhaps there's a hidden Omni configuration variable that will override the current behavior, but you've probably got a better chance of finding out about it with email to the support ninjas.