Good question.
Total drivetrain efficiency of the electric cars are in the high 50's to the mid 60%'s. Multiply that by losses from the powerplants-grids and the overall drops to 20 something %, begging a solution like you mentioned.
However, a tangent political issue is PDJT making a move the other day to shore up Coal & Nuclear, hmmm what do they know that we don't.
IMHO?
A Co-Generation / Combined-Cycle powerplant in your basement ( Honda has one NOW ) that burns Natural Gas from Fracking and the small natural gas fired engine spins the generator for your Home and Electric Cars electrical needs, and the waste heat heats your hot water. The rest can be done via heat pump of the juice you create with efficiencies in the 60%+ region.
It might be tougher w/ the Heat Pump in northern climes, however I am sure another source for heat can be added to make that work.
Interesting disruptive times ahead...
I thought electrical drive train efficiency is almost 100%.
So... you are saying the problem of electrical infrastructure can be partially addressed with a greatly expanded natural gas infrastructure. I wonder what the relative costs would be.