The fallacy doesn't make a value judgement. It points out something counterintuitive about the accuracy of a filter or test. That thing is important, but not dispositive. If the base rate is low and the false positive rate is percentagewise high but the overall number of hits is manageable, low-power statistical tests can have utility as pre-filters.
I have the same thought every time I go through airport security ("whoever designed this probably doesn't know about the base rate fallacy"), but if the system is only ejecting 1-2 candidates per station per hour for expensive "offline" screening, it's not untenable.