The White Council assaults Dol Guldur?

[Kuruharan]

It just strikes me as odd as well, as you'd think that Gandalf et al would be able to detect one of the Nine pretty easily. Why all of the snooping around and spying? Surely a few elves and wizards could clean house, as it were, if it were simply one (or all) of the Nine.

I'm not sure I agree.

I guess it depends on what you mean by "detect". Detect isn't the same thing as identify.