I'm pretty sure that if car insurance were somehow banned, especially medical-liability, fewer people would own and operate motor vehicles.
Insurance exists to put an upper bound on risk; the bad thing will hurt or be inconvenient, but with insurance it won't kill you. Perverse incentives appear in the case where the insurance payout is greater than the inconvenience/pain of the insured event. Until that threshold is breached, however, I don't think there's a case against insurance (and insurers that inadvertently pay people to have accidents rapidly go out of business).