I am someone who keeps the option of reopening old tabs on launch set to on. But if I close the normal window while private browsing window is on and reopen it, the old tabs disppear and a fresh window is opened with nothing inside. I have to follow an elaborate set of steps to ensure everything apart from the normal window with tabs is closed first including the private window, and then close the nomal window with my tabs at the end so that the tabs can be recovered when I open it next time.
I want any connection between the private window and the normal window to be gone so that these two windows are not dependent on each other at all and act like two separate browsers. Given that there is a option for adding private window to taskbar separately, I think this should also be considered.