Why do governments allow a substantial cost of automobile collisions to fall onto all of society?

This premise applies to the USA, but I wouldn't be surprised if isn't similar is other countries.

In the USA, an estimate of annual damages related to automobile collisions at the low end is $300 billion.
An estimate of annual insurance payout is at the high end is $180 billion.
This means in a best case scenario, the cost that is put on society is $120 billion annually. This falls onto all people, not just drivers.

I can see that governments do not want to insist that drivers are 100% accountable for the damages for their mistakes.

What are the legitimate reasons why government would spread out this cost burden rather than insist of full accountability?

I can only thing of one: Governments cannot fairly price automobile costs for lower income individuals because businesses need workers that can arrive to work by automobile.