You know, maybe we shouldn't, after all.
It's been almost a year since this proposal to burninate gm was made, and we still have (as of this writing) 88 questions tagged with it, more than half of which don't have any other gm-related tag.
Yes, it's still a big mess, with many questions using the tag gratuitously, just because the asker happen to be a GM, or a GM is somehow otherwise tangentially involved. But so are the other gm-related tags, too, and we can't just burninate all of them.
(Well, technically, we could. I'm just saying that we probably shouldn't.)
Part of the reason why the gm tag hasn't gone away, and also why it's stayed a mess, is that it had a simply awful tag wiki excerpt that just defined what a GM is, but offered zero guidance on how and when to use the tag:
"The Game Master runs the game, including having final say over how actions are resolved. Also referred to as Dungeon Master (DM), Referee, Storyteller, Master of Ceremonies (MC) or other titles, depending on the game."
I just submitted an edit suggestion to improve it, so that it'd recommend using the tag only for questions about the role of a GM, not for any random rules / play-style / etc. questions that just happen to somehow involve a GM (usually as the person asking the question):
"Questions about the role of the Game Master (a.k.a. Dungeon Master (DM), Referee, Storyteller, Master of Ceremonies (MC), etc.) in a role-playing game."
(As usual, further improvements are welcome; it's called a tag wiki for a reason.)
As it happens, that was before I found out about the existence of this burnination proposal. The edit is currently pending was just approved as I write this, and I do believe that it's an improvement even if this tag is to be eventually deleted, as it should at least cut down on its rampant misuse.
However, it also seems to me that, with a more focused tag wiki, further cleanup of the worst misuses and enforcement of its proper scope for new questions, this would actually make a perfectly good tag.
Furthermore, having a general tag for questions about GM-ing would allow us to tidy up the current mess of tags like gm-techniques, gm-preparation, new-gm and problem-gm.
In fact, there's now a proposal going on to burninate new-gm, and one of the arguments originally made in favor of its deletion (besides the fact that it's also a huge mess, and kind of meta by its definition) is that, when used properly, it's basically redundant to gm. (That proposal, which is now featured on the community bulletin, is actually how I came across the gm tag and, subsequently, this meta thread.) Meanwhile, the gm-techniques tag also has its share of problems, indeed not unlike those that have plagued this tag.
In fact, even at the risk of inviting downvotes by being too specific, let me present my own modest and tentative proposal for dealing with this mess of tags:
Keep gm as the general tag for questions about GM-ing. Remove it from any rules questions etc. where it's just used because the asker happens to be the GM.
Merge gm-techniques into gm; when used properly, those tags are all but synonymous. (Yes, gm-techniques is arguably a bit more specific, but IMO not enough so to warrant two distinct tags.)
Burninate new-gm as a pseudo-meta-tag (or mod-merge it into gm). As typically used, it's essentially synonymous with gm + "I'm a newbie," and even when not used so, it IMO still adds no significant value over just using gm, assuming both are cleaned up, anyway.
(This is probably the most controversial part of the proposal, so let me explicitly note that it's also an optional one. If the community feels that we really need a separate new-gm tag, then let's keep it; it'll be a bit redundant and meta-ish, but no more than it currently is.)
Leave gm-less, gm-preparation and problem-gm as they are for now. Yes, problem-gm has its, well, problems, but those are probably beyond the scope of this proposal. The others are, IMO, pretty much OK as they are.