It's not a meta-tag…
It's possible to use new-gm alone on a question. Consider the hypothetical question, "How do I start GMing?" Assuming it was asked in a way that wasn't too broad, it would need at least one tag, and the only one that would fit is new-gm.
Hypothetical demos aside, there are a number of questions we have where the newness of a GM is an inherent part of the problem, and those do justify the tag's existence. A hypothetical [experienced-gm] tag isn't symmetrical to new-gm: there are no problems inherent to being an experienced GM,† so it unlike new-gm it would only be a meta-tag for labeling the asker.
It's not a great tag, but it's not a bad tag either and doesn't deserve burnination.
† You could argue that being experienced can lead to becoming a hidebound GM, but that's being a problem-gm, not being an experienced GM.
… It's just being misused as one
For questions where the tag is being (mis)used only to indicate who is asking, or as an apology, the usual solution suffices: remove the tag.
To that end, the tag wiki should probably be worked on to emphasise that it's not for describing the asker, it's for tagging problems that are inherently entangled with being a novice GM. That won't stop it from being misplaced on questions, but correct tagging is the job of experienced users anyway and new-gm gets misused way less than a tag like dungeons-and-dragons, which we're fine with having to clean up after constantly. It only looks like a lot of misuse now because we haven't been paying attention and have let it get out of hand. Going forward, it'll be easy to keep it from being abused as a meta-tag, just like it's easy to keep dungeons-and-dragons from being used for the current edition. (Easier, actually, because we don't need to wait for the asker to clarify before we can fix misplacement of the new-gm tag.)
It's extremely valuable in Search
Unlike [beginner]-type tags on sites like SO, where searching on it would get you a useless mix of problems about disparate, unrelated programming languages, searching on the new-gm here effectively provides an ever-improving guide for new GMs. Provided we're curating posts properly and taking the tag off questions where it's being misused as a meta tag, what remains is a selection of common problems and pitfalls of novice GMs, with ready solutions.
Right now that search doesn't look so great here, but the tag is way overused and due for cleanup to eliminate its meta-tag mistags. A selection of our top-voted new-gm questions shows what we could have after cleanup:
See how awesome those are, when they're grouped together like that and the unrelated questions are cut out? Quite frankly, I actually didn't expect them to be that great a list, but now that I see what the tag could be, what kind of resource we've been sitting on and neglecting, now I'm actually quite excited to tackle pruning the tag to bring out this list of awesome on the actual site.
We should keep the tag, and aspire to make it a small, well-curated set of questions that maintain high value and are immediately useful to someone learning (or stumbling over) how to GM, kind of like a set of frequently-asked... questions!
Besides which we'd have to keep it anyway, so no burninating
For discoverability, any replacement for the tag would need to have new-gm as a synonym, because that's the most natural phrase people think to type when looking for or asking the sorts of questions above (and why it was folksonomied into existence originally). Burnination prevents the tag from being re-created, so what we'd end up with is more people just putting the reviled gm tag on more things for lack of any other tag they can find.
I don't think we can synonym or burninate our way out of people trying to label themselves in the tags. For a tag that has a mix of good non-meta uses and bad meta uses, burnination doesn't improve the situation and might make it worse. That brings it back to the same conclusion as way up above: it's our job to fix question tags that new users misapply. We do it all the time, and adding new-gm to the "regular offenders" is a drop in the bucket.
- Leave the tag alive because it's useful,
- clean the ever-loving crap out of our questions that only (mis)use it as a meta tag,
- then just keep it in mind during the usual cleaning edits on new questions.
The questions that still have the tag after that will be a collection of solid gold awesome.