Well, that's a fairly complicated ethical question, isn't it? The general answer is "the point at which additional effort to reduce the number of false positives does more damage than it'd prevent"; I don't have the data to say exactly where that point is, but it's almost certainly higher than zero or epsilon.
So you would fire good teachers at random if you could also fire some disproportionate amount of bad teachers? That's strictly rationally better if we care only about student outcomes, but is worse if you care only about fairness to teachers.
Post will be returning in Main, after a rewrite by the company's writing staff. Citations Galore.