This is a feature, not a bug, and is pretty much intentional.
The reason:

• Sticky Notes doesn't run inside hildon-home, thus the only way to make the widgets re-appear on reboot is starting it in the background
• I want only one process handling all of the notes
• If you click on either the icon, or "add widget", the background process is called and it displays the new note
• When running in the background, it really doesn't do anything, just sits there doing nothing. It doesn't use CPU in this state, thus doesn't hurt your battery, either

I hope I could provide a meaningful explanation!
(I also added this one to the FAQ section of the original post.)