First though, it seems a misunderstanding has developed. I was not calling the competence of the UW lab into question! They are bound by various state and federal regulations and I'm certain are doing the absolute best that they can under the circumstances. The examples I provided were to illustrate just how absurd the current state of affairs is, and to make it clear that bureaucratic ineptitude is to blame.
We obviously both agree that QA/QC is necessary; note that my back-of-the-envelope calculations included controls. I don't pretend to know precisely what requirements FDA regulations place on various diagnostic tests. What I do know, and attempted to illustrate in concrete terms, is that it is physically possible to scale testing in a sufficiently reliable manner using common instrumentation and bulk reagents. Any genuine attempt to explain US testing shortages _must_ account for this fact.
Yes, parallelizing sample prep requires a sufficient number of properly trained technicians. Presumably the US government is capable of locating and making use of qualified personnel in an emergency situation such as this? (To start with, literally any graduate student whose research includes running molecular biology protocols is likely over qualified for sample prep.)
Regarding serial numbers and labeling, it is indeed trivial. You can literally keep a list on paper and label tubes by hand (I did this for years in an academic lab). This step is fast compared to overall sample prep time.
I have no idea where you got the idea of a barcode migration from. Remember, I'm not describing a clinical lab operating according to FDA regulations; I'm describing a sufficiently reliable setup that closely resembles an academic research lab and would maximize throughput in an emergency situation. The only goal is to receive a package, label a corresponding tube, run a test, and report the result.
(BTW, I claimed that bench space for sample prep, not instrument throughput, was likely to be the bottleneck. In fact, instrument throughput not being the bottleneck was one of my primary points.)