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It’s a somewhat stupid example, because nobody endangers their own life just because they have health insurance.

Smoking instead of reckless driving may make it (slightly) more understandable.

Sure, though, to be pedantic, a common example of moral hazard is the increased likelihood of driving recklessly in the presence of mandatory seat belts. See https://web.stanford.edu/~leinav/pubs/RESTAT2003.pdf

That’s not a moral hazard. The word doesn’t even appear in the paper. It’s just an example of somewhat efficiently choosing a different point on the risk/reward continuum when the payoffs change.

A moral hazard is choosing a selfish course of action with negative external effects.

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