I don't think the proof tag conveys any useful information. Sometimes, it excuses the asker from adding a more descriptive tag, like in this question which is really a linear algebra question but is only tagged proof. Should we get rid of the tag? Can we get rid of it without bumping all its tagged questions to the front page?
(Note that we do have a proof-theory tag for actual proof-theoretic questions.)
P.S. I was sure I had seen a previous post on meta asking the same question a long time ago, but I can't find it any more. My apologies if this is a duplicate.
The reason these tags are a problem is that meta-tags do not describe the content of the question. They describe some other aspect of the question, like the author's skill level, or the author's motivation for asking it, or generally what "kind" of question it is (poll, how-to, etc.).
Meta-tags are actually a subset of a larger problem that I usually call dependent tags. These are tags that don't say anything by themselves - you can't tell what the question is about unless they're paired with some other tag (or several of them). These tags are a problem because people don't realize this and will often use that as the question's only tag.
The only potential justifications of proof proposed so far, by Arturo and
svenkatr, would make it quite clearly a meta-tag, and such tags are explicitly discouraged (see aforementioned SO blog post).