Scholarship and public benefit:
As a social science PhD student I frequently encounter discussions about the need for "public scholarship" in the humanities and humanistic social sciences. Often these discussions highlight the importance (and occasionally the hazards) of publishing in non-academic forums so that scholarly work can benefit the public or "publics." My understanding is that such forums might include more traditional online media (bracketing the question of whether such outlets are typically accessible to researchers at very early/pre-doctoral career stages), but the focus is usually on freely available and accessible works published on, e.g., institutional or self-hosted blogs, sites like Medium.com, perhaps small free weeklies, and probably other sorts of places I'm forgetting or not familiar with.

My understanding is that putting one's ideas on the internet in quasi- and non-refereed forums doesn't hold much water in most disciplines, at least in terms of applying for a job in academia. And my sense is that advocacy for making one's research available in these ways is fairly new, so I'm not sure the ambivalence/apathy/disdain for such practices has been at all overcome even in disciplines where it's being promoted.

This skepticism notwithstanding, perhaps a case could be made, at least in the humanistic social sciences and humanities but really in any discipline, that doing work where one employs the critical thinking and research skills that are part of academic training is beneficial to the public (particularly if done, say, on an unpaid basis) and even to the scholar, whether or not that work might be officially deemed "scholarship" or "research" as traditionally conceived.

The question:
Instead of including relevant, published non-academic writing or similar work on a CV as (public) "scholarship" or "publications" per se, would it be reasonable, and compelling, to include it elsewhere, perhaps under volunteer work? It seems analogous to an item I already list under volunteer service—work I've done at a local food cooperative, which I list because a position I held there directly relates to and informed my research. (And I think that's a reasonable entry for volunteer work, but come to think of it I'm not entirely sure.)

If it's reasonable to list under volunteer work informal writing/publications relevant to one's research, might one such item be contributions to Stack Exchange—and hear me out, here—if such contributions were related to one's field? For example, if a student of economics or mathematics or linguistics regularly contributed to related SE sites, could that contribution be considered a public benefit, a contribution to the scholarly community, a point of public-academic interface, etc., and thus plausibly listed on a CV? Not in the sense of listing individual posts as "publications" but simply a single line item like "site contributor" or the like?

For context:
I ask this primarily because I've never been in the position of reviewing CVs for (academic) job applications or funding requests, so I don't have much of an idea what's plausible versus what comes off as obvious BS.

I haven't seen enough CVs to recall off the top of my head whether volunteer work is a terribly common section on a CV, but I do know that on at least one federal grant application, among the meticulously specified limitations and requirements for the CV, there are a total of four sections and one is essentially volunteer or other non-academic work related to one's research.

I'm a PhD student in anthropology at an R1 institution. I plan to apply for academic positions, aiming for a research university. I'm about to start fieldwork for my dissertation project, so I'm not really at a point where publication is expected, but I've been thinking about publication recently because I've got severe writer's block (everywhere but here). Although I anticipated having at least one paper under review at this point, I don't, and as my project progresses the few things (e.g. term papers) I've written that could potentially be revised for submission seem increasingly irrelevant to my research (and reading my own papers a year or two later makes me cringe). I don't mention this because I'm thinking blog posts or SE or whatever could be a substitution for publications, but after recently joining SE I've been spending way too much time on SE sites as I procrastinate doing all the work I have piling up, so perhaps I'm harboring just a tiny fantasy that all that time, including the hour I've been writing this question and the many hours I will doubtless spend on SE in the coming months and years, will be a marginally justifiable tradeoff.

Note: I considered asking this question on meta but opted for here since it's about SE in general in relation to academia.

Edit: my question is similar to this one about SO/SE reputation but I think sufficiently different: mine isn't about reputation per se but rather participation generally, and the inquiry and already-existing answers here have specifics related to publication and public benefit/engagement that aren't addressed by the previous question (although vaguely referred to in one of its answers). And—not to say older questions/answers are necessarily always in need of update, but—in the intervening eight years it's possible the landscape has changed a bit in terms of evaluating CVs that list participation in question and answer sites or other online forums.

 This question about communicating SE achievements on a CV or in an interview is more similar, but that question assumes SE activity is relevant and asks how to frame it as an "achievement." The shorter answer there gestures toward what I'm asking here, but the longer answer focuses specifically on the metrics of SE vs. those used in academic evaluation, and my question is more about the nature of SE participation (independent of SE metrics) especially in light of recent calls for academics to engage in more "public scholarship."

Scholarship and public benefit:
As a social science PhD student I frequently encounter discussions about the need for "public scholarship" in the discipline. Often these discussions highlight the importance of publishing in non-academic forums that can benefit the public. My understanding is that such forums might include more traditional online media but the focus is usually on freely available and accessible works published, for example, on institutional or self-hosted blogs or sites like Medium.

The question:
Instead of listing publicly available non-academic writing on a CV among traditional publications, it seems reasonable to include it elsewhere, e.g. with other volunteer work. Would you find it justifiable if, for example, a student of economics or mathematics or linguistics who regularly contributed to related SE sites listed that contribution on a CV (under volunteer work or elsewhere) as an example of scholarly work with a public benefit? Or perhaps the more relevant question: would you anticipate that colleagues who are not familiar with/frequent contributors to SE would find this a reasonable and even compelling inclusion?

The context:
I don't recall seeing volunteer work listed on full-length academic CVs, but I know that CVs for some grant applications have space for it. I ask this primarily because I've never been in the position of reviewing CVs for (academic) job applications or funding requests, so I don't have much of an idea what's convincing or relevant versus what comes off as BS or fluff.

Non-duplication:
The question I'm posing is related to this one about SO/SE reputation but sufficiently different that it is not addressed by answers there. My question isn't about reputation per se but rather participation generally, especially in the eyes of CV reviewers who may have no idea what SE is and what "reputation" means on the site.  This question about communicating SE achievements on a CV is also vaguely similar, but the longer answer there focuses on SE's metrics and answers unrelated to "scholarly" output (e.g. questions about working conditions, rather than answers related to the subject matter of one's discipline). I'd also note that those questions were posed 9-10 years ago, and in the intervening time there have presumably been changes in how people view the academic and professional relevance of online, non-academic publications.

What most substantially sets my question apart from others relates to its concern with framing SE contribution as publicly available scholarly output—in anticipation, say, of a CV reviewer who wonders, "What work have you done that's related to your research but has had a benefit for people outside the university sphere?"

Edit: my question is similar to this one about SO/SE reputation but I think sufficiently different: mine isn't about reputation per se but rather participation generally, and the inquiry and already-existing answers here have specifics related to publication and public benefit/engagement that aren't addressed by the previous question (although vaguely referred to in one of its answers). And—not to say older questions/answers are necessarily always in need of update, but—in the intervening eight years it's possible the landscape has changed a bit in terms of evaluating CVs that list participation in question and answer sites or other online forums.

This question about communicating SE achievements on a CV or in an interview is more similar, but that question assumes SE activity is relevant and asks how to frame it as an "achievement." The shorter answer there gestures toward what I'm asking here, but the longer answer focuses specifically on the metrics of SE vs. those used in academic evaluation, and my question is more about the nature of SE participation (independent of SE metrics) especially in light of recent calls for academics to engage in more "public scholarship."