Keep stylesheet open after a notebook is closed

Question

I find this behavior annoying:

path = FileNameJoin[{$HomeDirectory, "Desktop", "stylesheet.nb"}];

Export[
 path,
 Notebook[{
   Cell[StyleData[StyleDefinitions -> "Default.nb"]],
   Cell[StyleData["Notebook"], Background -> LightBlue]

   }]
 ]

 nb = CreateDocument[];
 SetOptions[nb, StyleDefinitions -> path];

 NotebookOpen@path

So, now we have a notebook and its stylesheet opened and can play with edits. Notice that I haven't invoked the stylesheet via Format/EditStylesheet menu item but manually.

So now close the nb.

Stylesheet is automatically closed too. How to prevent this? Should this happen?