Just a thought, but how about letting privileged users vote to keep a question open, which would negate some number of close votes? (As well as a delay before closing, even once the votes were obtained.) Also if someone is in the process of writing an answer, that should count against closing.
I tend to agree with the OP that sorting and filtering are a better solution to maintaining quality than unnecessarily closing marginal questions. However, some questions certainly need to be closed. The problem (or at least a problem) seems to be that with such a large number of privileged users, hitting a 5 vote threshold is not difficult, even if the question doesn't deserve to be closed. Increasing the threshold would be one solution, but would make unnecessary moderation work. A don't-close vote seems like potentially a better solution.
I tend to agree with the OP that sorting and filtering are a better solution to maintaining quality than unnecessarily closing marginal questions. However, some questions certainly need to be closed. The problem (or at least a problem) seems to be that with such a large number of privileged users, hitting a 5 vote threshold is not difficult, even if the question doesn't deserve to be closed. Increasing the threshold would be one solution, but would make unnecessary moderation work. A don't-close vote seems like potentially a better solution.
Edit: Unsurprisingly, looks like I'm not the first one to have this idea: https://meta.stackexchange.com/questions/125/how-about-a-vot...