You have no choice:
http://en.wikipedia.org/w/index.php?title=Special%3ALog&type=delete&...
There is nop humane way to check to see if all those deleations were correct and within policy.
Well, we can do deletion log patrol, just as we do recent changes patrol at the moment. Spotting the vandalism isn't too hard, it's cleaning up after it when you have no greater powers than the vandals which is hard. It's not impossible, and if we would get significant gain out of giving everyone access to the delete button then it might be worth it, but we would get very little gain, so it's simply not worth the hassle.