But it's still preferable to the one that didn't alert you the one time it really needed to.

A test with a high false positive rate can be combined with other tests to give a better picture. A wave detection plus a seismic event is a lot more compelling than either on their own, so long as non-seismic "tsunami" detections and non-tsunami causing seismic events tend to be independent events.

A false negative on the other hand at best might be dismissed if you have enough other evidence, but more than likely will make you stop looking at more data. A zero false negative rate is likely unachievable, and the perfect is the enemy of the good enough, but false negatives are a much worse issue to deal with than false positives.