I think this is a little more pessimistic than what the piece says. The NeurIPS (then-NIPS) experiment said that about 60% of papers accepted by one PC got rejected by the other. That doesn't actually mean "the quality of the work has little to do with its odds of acceptance". It may just be that there's a paper has to cross a quality threshold, and once it's past, then the outcome has a lot more variation.
My personal take on NeurIPS specifically is that there's a fraction of bad papers, maybe 40%, that probably shouldn't and won't get in. Then there's a minority of very nice papers that probably should and will get in, maybe 5-10%. And then there are a bunch of middling papers where a lot of it is luck and drawing friendly reviewers. But these aren't bad papers, and you can't really just churn them out, they're just not very good papers.
From memory, it was 25% rejected by both PCs, 15% accepted by both PCs, and the middle 60% random.
As you mention, the problem with having two sets of reviewers is that it's hard enough for conferences like NeurIPS to find one set of qualified reviewers. Usually at least 1/3 of reviewers on any given paper produce a poor review, either because they don't care or because they really lack expertise. Complaining about this is so widespread that it even doubles as a sort of icebreaker for researchers, but nobody has a good solution.
Essentially if you look at review scores for a conference which has say a 40% accept rate (and this is quite similar across fields I'd imagine), you find there's 10-20% (depending on conference) of papers that are clear reject for all reviewers, then there's probably around 10%-15% of papers which are very clear rejects now the rest of the papers are very similar in scores so the cut-off becomes quite arbitrary (and depends on luck as well). This is actually well known for grant applications and a sign that there is likely not enough money in the system.