Uber does have insurance for its drivers. And in places where it dosent you are requored to have a commercial insurance policy. Otherwise they could be sued because the driver is their employee driving at their behest.
The biggest issue is insurance companies not being willing to cover paying customers for fear that they will actually habe to pay out on a claim. Since they love taking our money but will grill you to death over a claim. They literally find any way possoble to deny your claim then pay to pass laws that force your to get insured.