Because insurance typically affects all victims of a potential accident, and this includes people on crosswalks, in other vehicles and riding bicycles along the road.

If the insurance company deems you 'uninsured' this will result in society picking up the bill.

So the rights of individuals to choose to pick a seller who in that case is uninsured can have consequences for parties other than the two involved in the transaction.

jacquesm's comment is correct. Someone operating a taxi on domestic insurance may find that they are not covered if they collide with someone while they have an Uber passenger. The uninsured uber driver is then unable to pay for the damage to the other driver's car. That damage may be covered by their own insurer (increasing everyone's premiums) or they may be left out of pocket.

Because accidents are too violent and too infrequent for post-hoc enforcement to work. By making it illegal to drive without insurance police can do enforcement continuously, creating an incentive for insurance enrollment before you get hit by a car.

If you have to wait for peoples' lives to be ruined for you to have an opportunity to create your incentives, it's already too late.