Assuming that the distributions are exactly equal, the test would still give misleading results in situations in which the bias does not manifest as a different

Assuming that the distributions are exactly equal, the test would still give misleading results in situations in which the bias does not manifest as a different cutoff. For example, if a VC funds all male founders but flips a coin to decide whether to fund each female founder, the test would fail to detect overwhelming bias. Obviously that specific scenario is not realistic, but I believe something like this is plausible enough: A VC funds all male founders who are considered promising, and all female founders who are considered promising AND went to school with one of the partners. And it's not hard to imagine a plausible scenario in which the test would give false positives rather than false negatives.