This is wrong. Wikipedia was working right from the
start, even before
adminship existed.
It only worked because the vandals hadn't found it yet. If you removed
adminship from Wikipedia now, we would not be able to control the
vandalism. Obviously, I have no way to prove that, but I'm confident
it is the case.
You're also forgetting that Wikipedia is not the
only wiki, and that
MediaWiki is not the only wiki engine. Most other wiki engines do not
have an "admin" user level at all, and last I checked the Pattern
Repository was still working just fine.
The English Wikipedia is by far the biggest and best known wiki, and
as such is the biggest target for vandalism.