Do you have a source for the 10-20%? ICEs are incredibly inefficient, and I wouldn't be surprised if the grid was twice as efficient, although I too have no source to back it up.
> The total WTW efficiency of gasoline ICEV ranges between 11-27 %,
> diesel ICEV ranges from 25 % to 37 %
> The EV fed by a natural gas power plant shows the highest WTW efficiency which ranges from 13 % to 31 %
> While the EV supplied by coal-fired and diesel power plants have approximately the same WTW efficiency ranging between 13 % to 27 % and 12 % to 25 %, respectively
> diesel ICEV ranges from 25 % to 37 %
> The EV fed by a natural gas power plant shows the highest WTW efficiency which ranges from 13 % to 31 %
> While the EV supplied by coal-fired and diesel power plants have approximately the same WTW efficiency ranging between 13 % to 27 % and 12 % to 25 %, respectively
https://ui.adsabs.harvard.edu/abs/2020SJRUE..24..669A/abstra...