I'm also a PhD[0] and researcher who has worked in various fields, including national labs too (You DOE?)
I mostly share the same sentiment, and I see a similar issue with the product. The current system is not in its current poor state due to lack of reviewers, it is due to lack of quality reviewers and arbitrary notions of "good enough for this venue." So I wanted to express a difference of opinion about what peer review should be (I think you'll likely agree).
I don't think we are doing the scientific community any service by doing our current Conference/Journal based "peer review". The truth is that you cannot verify a paper by reading it. You can falsify it, but even that is difficult. The ability to determine novelty and utility is also a crapshoot, where we have a long history illustrating how bad we are at this. Several Nobel prize worthy works have been rejected multiple times due to "obviousness", "lack of novelty", and "clearly wrong." All three apply to the paper that led to the 2001 Nobel Prize in Economics[1]!
The truth of the matter is that peer review is done in the lab. It is done through replication, reproduction, and the further development of ideas. What we saw around LK-99[2] was more quality and impactful peer review than what any reader for a venue could provide. The impact existed long before any of those works were published in venues.
I think this came down to forgetting the purpose of journals. They were there when we didn't have tools like ArXiV, OpenReview, or even GitHub. Journals were primarily focused on solving the logistic problem of distribution. So I consider all those technical works, "preprints", and blog posts around LK-99 replications as much of a publication as anything else. The point is that we are communicating with our peers. There's always been prestige around certain venues, but primarily people did not publish to them. The other venues checked for plagiarism, factual errors, and any obvious errors. Otherwise, they continued with publication.
This silly notion of acceptance rates just creates a positive feedback loop which is overburdening the system (highly apparent in ML conferences). The notions of novelty and impact are highly noisy (as demonstrated in multiple NeurIPS studies and elsewhere), making the process far more random than acceptable. I don't think this is all that surprising. It is quite easy to poke flaws in any work you come across. It does not take a genius to figure out limitations of works (often they're explicitly stated!).
The result of this is obvious, and is what most researchers end up doing: resubmit elsewhere and try your luck again. Maybe the papers are improved, maybe they aren't, mostly the latter. The only thing this accomplishes is an exponentially increasing number of paper submissions and slowing down of research progress as we spend time reformatting and resubmitting which should instead be spent researching. The distribution of quality review comments seems to have high variance, but I can say that early in my PhD they mainly resulted in me making my works worse as I chased their comments rather than just trying to re-roll and move on.
In this sense, I don't think there's a "lack of reviewer" problem, so much as we have an acceptance threshold problem with an arbitrary metric. I think we should check for critical errors, check for plagiarism, and then just make sure the work is properly communicated. The rest is far more open to interpretation and not even us experts are that good at it.
[0] Well my defense is in a week...
[1] https://en.wikipedia.org/wiki/The_Market_for_Lemons
[2] https://en.wikipedia.org/wiki/LK-99