What's "the insured event" here? If it's the enactment of legislation, then yes, it is possible in principle that insurance will affect the market for laws, by shifting risk to those most able to bear it. If it is the behavior of people who would be affected by legislation (say, a breach of some kind which gives rise to liability), then my above point stands: the "impact of moral hazard problems [is] reduced" iff insurance does not change behavior much.

Liability insurance only covers negligence and strict liability, not intentional torts; and insurers seek to minimize their payouts by (a) imposing deductibles and (b) monitoring their clients' observable precautions. In some cases, insurance will actually enhance the incentives inherent in tort law, by shifting part of the risk of negligence to a third party which can specialize in monitoring against it; but this is a matter of technical efficiency.