Uber and Lyft both now verify that you have supplemental insurance. It's kind of screwy. If you have a passenger in the car, Uber/Lyft coverage is in place. If you are driving around working but no passenger, it's the driver's rideshare insurance - which is typically a rider on their personal policies. This probably changes regionally, but that's how it works in California.
Which is a good first step... but if I'm injured at a regular job? workers comp will cover my own bills and lost wages while I recover(usually even if it was my own goddamn fault) - Uber drivers don't get that benefit, and they are a lot more likely to be injured on the job than I am.