> The South Pole is a smaller population than China so I'd be worried about false positives
Even if the false positive rate is really low, it's still a problem. All of these dragnet-style things mess with your priors. In a traditional investigation, the police have a handful of suspects and then gather evidence. Circumstantial evidence showing that the chances are 1 in 1000 that this one of the five suspects was not the culprit is pretty convincing, and probably enough to convict.
Cast a dragnet over a city of 1 million, and suddenly that same 1-in-1000 error rate will be giving you 1000 innocent people who, under the old system, are 'guilty beyond reasonable doubt'. They've been pre-selected to look pretty frikkin' bad regardless of whether they're guilty, which means any one of them will have a hell of a time proving their innocence.