One of the main reasons that car insurance is required by law is because your vehicle moves and has the potential to cause injury and damage to other people. Since your home is a fixed object there is no legal requirement that you maintain insurance on it.
Coverage & Claims
In most single-vehicle accidents, the driver involved is normally considered at-fault because there simply isn't another person on which to place blame. The situation might have very well gone in your favor if the other driver had made contact with your vehicle, but it would be next to impossible to prove the other driver was the reason for the accident when no other vehicle is damaged.
Car Insurance Costs
Consider the golden rule here. If you are involved in an accident and the other person is at fault, wouldn't you expect them to pay for your damages?
As of May 2015, 42 states allowed for digital proof of insurance rather than a paper ID card. That is seven more states than in 2013 so there is potential that within the next few years every state could allow for digital proof.