I don't think it costs anywhere near $10/hour to operate a passenger vehicle, even after insurance and maintenance.
The IRS sets a standard rate of 58 cents/mile for deduction of vehicle-related expenses. There’s obviously a wide range of actual costs, but that’s in the ballpark for an all-inclusive amount. If you average 20MPH then you’ll exceed $10/hr.
It seems large because we aren’t used to looking at TCO per mile, and only think about the cost of fuel.
The AAA average includes pickup trucks, which hopefully you wouldn't be using for Uber.
Edmunds puts the TCO for 5 years (includes insurance and gas) for a Prius @15,000 miles/year at $30,600. That is 40.8 cents/mile. 59c is 45% higher.
(This assumes you start with a brand new Prius; you may optimize better as an Uber driver)
Like is it really cost effective to go to the theater on the other side of town because the tickets are $1.50 cheaper? Or this grocery store versus the other?