No insurer would touch it.  It would cost more for the work involved in setting up the policy than they would ever realize in revenue.  

Cyclists create very minimal damage in society, especially compared with cars.  And any damage, which mostly impacts the cyclist themselves, is more than offset by the improved health outcomes we get from greater numbers of people cycling.  

The idea that cyclists need to be licensed and insured comes solely from a collective desire to punish people who do not fall in line with the dominant force in society.