People stop responding to warnings when the false positive rate is high.

For context: number of earthquakes which potentially may generate tsunamis is measured in hundreds per year across the planet. Number of potential tsunami events for any given "coast" is measured in single digits per year. In the hottest areas it is tens of events per year.

Right. If the system generates hundreds of alerts per day, and one of them was right one time, that’s not very useful no matter how cautious you want to be.

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.