I think it would only be a moral hazard if someone behaved irresponsibly because they have insurance. An alternate situation would be someone who was excessive

I think it would only be a moral hazard if someone behaved irresponsibly because they have insurance. An alternate situation would be someone who was excessively cautious without insurance but responsibly cautious with insurance. Or someone who behaved the same way but worried less due to having insurance. Since people tend not to make rational decisions when they are worried, insurance could even lower their risk. For example, my understanding is that many auto insurance companies cover windshield repair very generously because it reduces the risk that a customer will get in an accident trying to chase down a truck that kicked up a stone and damaged their windshield.