Even if academics could review all the papers on a preprint server (which the article argues -- rightly -- that they can't), it wouldn't solve the perceived problems (or the actual problems) with scientific peer review. The vast majority of irreproducible papers aren't detectible as irreproducible at time of publication. They look fine, and many actually are fine . They just don't reproduce. That's an expected outcom…
There is no place to make a note that something doesn't reproduce so its extremely time consuming or you need some source of tribal knowledge. In my postdoc I was trying to make some porous films and a bunch of paper's methods didn't seem to work, maybe I did it wrong, maybe some detail wasn't described, who knows. I couldn't get it to work and there was no way to document that failure.
1) It provides a reproducibility filter. If a method isn't shown to be reproducible, publically documenting that adds to the body of knowledge, and this would help drive an incentive towards reproducing work rather than just searching for novelty. It would document work that would otherwise be lost because there's no incentive to showcase it. When the lack of reproducible results isn't public, it's now more likely that others may waste considerable effort in the same vein.
3) It may enlist the original authors to help understand why the work didn't reproduce well. Maybe the secondary effort lacked some crucial step or understanding. The people best positioned to remedy this are the original authors, and this secondary publication incentivizes them to dialogue with those who couldn't reproduce the outcome. It doesn't mean they have to engage, but it at least gives them some reason to involve themselves in the process.