It seems like anyone could make an extension site to wikipedia where articles that aren't allowed at wikipedia could find a home, and the search there could also search wikipedia. The issue seems that nobody wants to put the hard work into making this happen, marketing it, and managing it. They just want wikipedia to do it for them, using the limited resources wikipedia has at their disposal, for free.
Going back to the brand management issue, I'd be OK with deleted articles and their history being moved to another wiki with a different URL, with a name that is not "Wikipedia". Cookies or some other mechanism could be used to manage user/session preferences so that users who want to to be redirected to this other, questionable-page wiki can be redirected when they try to access pages that don't fall in line with Wikipedia's editorial vision. I'd be fine with having huge in-your face warnings about the likely lack of quality or veracity of such entries... just as long as I can access that content.