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Few people would have problems with the deletion of true "noise" -- obnoxious and indecipherable solve-my-homework questions or obvious trolls.

But why delete a programming-related question with lots of healthy discussion and where people are enjoying themselves? Or, for that matter, a wikipedia page that is well-written and accurate, but only of interest to a small percent of people?

Not at all! It's fine to have an article on a topic that is only of interest to a small percentage of people, as long as those people have high edit counts on wikipedia.

My problem with this is that filters (e.g. search, tagging, ranking) give the same result without destroying information which is not, strictly speaking, noise.

No they don't, noise drowns out signal, see Google's problem with spam and splogs.

more like a high ratio of one person's preferred signal to other signals

By that metric, spam is signal because some people (spammers) want it.

They don't want it, they want people to see it.