A lot of taxis are already run 24 hours a day, switching off between drivers at shift changes. The per-mile gas, maintenance, and depreciation (ignoring any fixed per-day or per-year costs) are already much more than 10% of the total cost of a ride.
I came across a (possibly outdated) Uber pricing model for LA of a $5.60 minimum fare and a $0.90 per mile charge, and among other fees, NYC cabs are $2.50 per mile. Compare both of those numbers to the IRS mileage rate of $0.53 per mile to get a very rough lower bound on some of the costs.
The fare for NYC is incorrect -- $2.50 is the base price and $0.505/mile and $0.50/minute the car is stopped (i.e. in traffic if they're waiting). There's also a $1 surchage between 4-8pm on the weekdays.
I came across a (possibly outdated) Uber pricing model for LA of a $5.60 minimum fare and a $0.90 per mile charge, and among other fees, NYC cabs are $2.50 per mile. Compare both of those numbers to the IRS mileage rate of $0.53 per mile to get a very rough lower bound on some of the costs.