I agree with the critiques you make of specific papers (in section 2), but I'm less convinced by your diagnosis that these papers are attempting to manage/combat hype in a misguided way.

IMO, "underclaiming" is ubiquitous in academic papers across many fields -- including fields unrelated to NLP or ML, and fields where there's little to no hype to manage.  Why do academics underclaim?  Common reasons include:

1. An incentive to make the existing SOTA seem as bad as possible, to maximize the gap between it and your own new, sparkly, putatively superior method.
   Anyone who's read papers in ML, numerical analysis, statistical inference, computer graphics, etc. is familiar with this phenomenon; there's a reason this tweet is funny.
2. An incentive to frame one's own work as solving a real, practically relevant problem which is not adequately addressed by existing approaches.  This is related to #1, but tends to affect motivating discussion, whereas #1 affects the presentation of results.
3. General sloppiness about citations.  Academics rarely do careful background work on the papers they cite, especially once it becomes "conventional" to cite a particular paper in a particular context.  Even retracted papers often go on being cited year after year, with no mention made of the retraction.

I suspect 1+2+3 above, rather than hype management, explains the specific mistakes you discuss.

For example, Zhang et al 2020 seems like a case of #2.  They cite Jia and Liang as evidence about a problem with earlier models, a problem they are trying to solve with their new method.  It would be strange to "manage hype" by saying NLP systems can't do X, and then in the same breath present a new system which you claim does X! 

Jang and Lukasiewicz (2021) is also a case of #2, describing a flaw primarily in order to motivate their own proposed fix.

Meanwhile, Xu et al 2020 seems like #3: it's a broad review paper on "adversarial attacks" which gives a brief description of Jia and Liang 2017 alongside brief descriptions of many other results, many of them outside NLP.  It's true that the authors should not have used the word "SOTA" here, but it seems more plausible that this is mere sloppiness (they copied other, years-old descriptions of the Jia and Liang result) rather than an attempt to push a specific perspective about NLP.

I think a more useful framing might go something like:

• We know very little about the real capabilities/limits of existing NLP systems.  The literature does not discuss this topic with much care or seriousness; people often cite outdated results, or attach undue significance to correct-but-narrow philosophical points about limitations.
• This leads to some waste of effort, as people work on solving problems that have already been solved (like trying to "fix" Jia and Liang issues as if it were still 2017).  Note that this is a point NLP researchers ought to care about, whether they are interested in AI safety or not.
• This is also bad from an AI safety perspective.
• We should study the capabilities of existing systems, and the likely future trajectory of those capabilities, with more care and precision.

Some minor feedback points: Just from reading the abstract and intro, this could be read as a non-sequitur: "It limits our ability to mitigate short-term harms from NLP deployments". Also, calling something a "short-term" problem doesn't seem necessary and it may sound like you think the problem is not very important.

When I try to get the paper, I get a 404 error.

The paper makes a slightly odd multi-step argument to try to connect to active debates in the field:

This comment is some quick feedback on those:

Weirdly, this even happens in papers that themselves to show positive results involving NNs.

citations to failures in old systems that we've since improved upon significantly.

Might not be a main point, but this could be padded out with an explanation of how something like that could be marginally better. Like adding:

"As opposed to explaining how that is relevant today, like:

[Old technique] had [problem]. As [that area] has matured [problem has been fixed in this way]. However [slower deployment]/[more humans in the loop]/[other fix] would have reduced [problems]. Using [these fixes]/not making them critical systems which is risky because _ can help ensure [this new area] which [has the same problem] and probably will for [time] until it matures, does not have the same problems [old area] did [for length of time]."

But is that actually the right way to minimize the risk of harms? We should expect [that]

• Is there any empirical base which could be used to estimate this/provide information on improving things? Anything similar

We should expect the impacts of these technologies to grow dramatically as they get better

• What if the impact grows dramatically as...they get deployed widely? Even if it it's a bad idea, it's widely done because it's popular/cool/a fad/etc.?
• What approach would work best then?