From a 2003 study
we find evidence that automobile insurance has moral hazard costs, leading to an increase in traffic fatalities. We also find that reductions in accident liability produced by no-fault liability laws have led to an increase in traffic fatalities (estimated to be on the order of 6%). Overall, our results indicate that, whatever other benefits they might produce, increases in the incidence of automobile insurance and moves to no-fault liability systems have significant negative effects on traffic fatalities.
So, pedestrians who demand that cyclists be insured might be increasing their risk of injury (among other conclusions).