I guess I'm not persuaded by the premise of this. The premise seems to be that answers we're currently flagging as VLQ could be saved if they just went into a "help & improve" queue. Or, to state it more constructively: I think it'd help if you presented data to show how this would help.
When answers are flagged with VLQ, usually that's because the answer is so bad that there is no reasonable way to improve it (short of editing it to replace it entirely with something entirely new that's so good it could have been posted as a new answer). Typically, the right answer for those VLQ answers is to delete them.
When we have a terrible, very-low-quality answer, it seems like the right thing to do is to delete it. If you can see how to craft a good new answer from scratch, starting from nothing, then post it in the answer box.
And philosophically, if someone puts so little effort into their answer that it deserves a VLQ flag, then I have zero motivation to rescue their answer for them. I'm fine with helping and improving answers where the answerer has put in 80% of the work, and needs help for the remaining 20%. But if the answer has put in 0% of the work, and reviewers are supposed to put in 100% of the work, then I don't think that's a reasonable thing to ask reviewers to do. In my experience, usually when you've got a VLQ answer, turning that into a good answer is no easier than writing a good answer from scratch.
That's my anecdotal impression. I could be persuaded by data showing that my impression is wrong. Do you have data? Perhaps you could do a review of answers that have been flagged VLQ, and analyze them to see if my sense is correct?
Let me comment on a few other issues raised in the post:
You asked what the difference between VLQ and NAA flags is. There is a difference. NAA is for answers that don't even try to answer the question. If you've got an answer that is trying to answer the question but is total garbage, you need to use VLQ, not NAA. VLQ shouldn't be used to flag answers that are merely wrong, but if it's got severe problems that can't be rescued through editing, then a VLQ flag can potentially be appropriate. For instance, I've seen answers where they are only one sentence long, the answerer thinks they're trying to answer the question, but the reasoning is gibberish or reflects a fundamental irreparable confusion. For some such answers, a VLQ flag is appropriate, as a way to get enough 10K users to take a look and vote to delete.
So, when you say that anything currently flagged with VLQ could instead just be flagged with NAA, that's simply not correct. In my experience, many of those NAA flags will be rejected.
- I'm concerned whether flagging "needs improvement" will be effective. It's a one-bit signal, but doesn't indicate what specifically needs to be improved or how to do it. It's not actionable. It's just a flag saying "this sucks" but without explaining exactly how it could be better. I'm not opposed to it, I'm just not sure whether it's going to work well enough in practice to justify the development effort.