I think to authors are overly optimistic in our ability detecting highly dilute samples. Pooling studies in Dengue Fever using RT-PCR found sensitivity fell faster than could be explained by dilution effects alone. At 100:1 or 20:1 pooling the false negative rate will be unacceptable.
In general, titers of the virus in NP swabs should be high enough to withstand 10, maybe 20-plex pooling. However, as you allude to, there are plenty of other effects that can influence PCR. If there is one sample, for example, that contains a PCR inhibitor, like heme, it may then inhibit all the samples it is pooled with.
Additionally, swabs are not just swabs of virus, they also pull of highly variant amounts of bacteria and human material. These things may also affect the efficiency of PCR.
That would be a very effective way to achieve herd immunity quickly. Typically the swab is stored in a liquid viral transport medium. You perform a RNA extraction on this liquid, pool the product and run RT-PCR on it.
The interview covers this to an extent, the reason is a lack of appreciation of the potential and an overestimation of the complexity. It’s a somewhat complicated thing to multiplex all the samples correctly, it’s too complex a scheme for an individual lab scientist to do, it either requires a robot or some form of semi automation, I think in Rwanda they were using a smartphone app to tell the scientists which batch to put each sample in. I think that if you could convince the worlds public health bodies, and we can get saliva sampling off the ground in combination you could get to the levels of testing needed to actually do national level surveillance.
Edit: false positive -> false negative