Thank you for writing out this argument! I had a quick question about #2. The earlier a pandemic would be caught by naive screening, the quicker its spread is likely to be. So despite the fact that early detection might buy less time, it might still buy plenty of value because each doubling of transmission occurs so quickly.
This still depends on mitigating the concerns you raised in #1 and #3, though.
Thanks for the post! This may not be helpful, but one thing I would be curious to see would be how the dispersion coefficient k (Discussed here; I’m sure there’s a better reference source) affected the importance of having many sites. With COVID, a lot of transmission came from superspreader events, which intuitively would increase the variance of how quickly it spread in different sites. On the other hand, the flu has a low proportion of superspreader events, so testing in a well connected site might explain more of the variance?