Driving a battery-powered electric-vehicle on electricity produced by fossil fuel could be some percentage of efficiency gain. For instance, gas-turbines at electric powerplants often run for long periods of time at fixed speeds and that's an efficiency gain. Also, the gas-turbines at powerplants can make use of waste heat which is another efficiency gain. Another possibility is for natural-gas to be reformed to gray hydrogen and then the gray hydrogen run in fuel-cells at the electric powerplants. Certainly, compare the efficiency of hydrogen fuel-cells to gas-turbines for electric powerplant use.
The problem with battery-powered electric-vehicles is that they are primarily developed and designed for required driving ranges and that's a potentially wasteful development. Other types of vehicles could just change the size of the fuel tank for different driving ranges and that's not primary development and design.
Finally, the electric powergrid is only expected to be 45% renewable electricity at the year 2050. Much of the problem is that the transition to battery-powered electric-vehicles will increase demand for electricity. Now if the renewable electricity is accounted to buildings and houses then the non-renewable electricity could be accounted to battery-powered electric-vehicles !
I can add primary sources. This first source says that 450GW of European offshore wind-power will be 30% of Europoean electricity demand in the year 2050 and that result because demand will have grown 50%. However, the current amount of European offshore wind-power is only 20GW.
https://windeurope.org/about-wind/reports/our-energy-our-future/
Down in their assumptions they improve the numbers by saying that there could also be 650GW of European onshore wind-power. I suppose my number used 650GW as the total but I'm going to check that point again and then edit.
This second source says that U.S. solar-power could be 40% of demand in the year 2035. However, current U.S. solar-power is only 3% of current demand while full demand is expected in the year 2050.