Is moral hazard immoral?

Not in the way that economists use it. Long ago, it used to mean

that reducing risk too much exposed people to the hazard of poor moral judgments. If an insurer charged too little for a policy to replace farms in the English countryside, Farmer Brown might be less careful about cows knocking over oil lamps in the barn.

In time, the economists got their hands on "moral hazard," and the first thing they did was strip out the heavy moral freight to make the concept value-neutral. Now moral hazard became less about judgment and more about the economic "inefficiencies" that occur in riskless environments.