Detailed records and redundancies ensure you don't mix up any of the tens of thousands of samples coming in. These systems are crucial for being able to scale up as they have without complete chaos breaking out in the lab.
You are right that barcodes are far more efficient, after implementation. But implementation takes months, and requires diverting resources that would otherwise be used to run more samples. The lab would face significant downtime putting a barcode setup in place and retraining. (See nkrumm's comment about labs not having a "test" environment.)
> Standard qPCR machines are incredibly common in both academia and industry and have 96 wells at minimum. The protocol published by the CDC has an 80 minute runtime. That's 1000 tests per day for a _single_ low-end machine.
That's only if we ignore the sample preparation time (orders of magnitude longer than analysis time), and the many control wells necessary to ensure the technique was successful. While I suspect these will also be dismissed as bureaucratic inefficiency, they're needed to make sure your newly-installed instrument running 24/7 hasn't broken down, and that the high throughput sample prep wasn't botched for a given prep batch.
The stakes for these tests are high enough that cutting corners on QA/QC isn't acceptable, because it means more lives lost. Doing a mediocre job for testing at this scale will have a very real impact on our population.