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Putting everything else aside for a second, having tests that are very sensitive, even if it means a lot of false positives, is the best tradeoff when the goal is to prevent a disease to spread.

I mean, what's the alternative? Having tests that are less sensitive would have lead to fewer people quarantined unnecessarily, but it would have also lead to more contagious people not being quarantined, making it even less feasible to contain this dumpster fire.

The goal in such a scenario isn't to get an accurate count for the public and media to jerk off to, even though that's exactly what happened. The goal is to end a pandemic and to "flatten the curve". Clearly that could have worked better, but less sensitive tests would have not been a contributing factor to that.