No, it's stupid. You have higher private costs because you spend all days long at home.
More than driving to and from work? The cost of manufacture, the tyres, the burning of fuel?
My wife works at home, and heats it all day. It's actually more green for me to work from hom as well in that case, but my employer needs me at a location. So I have to drive (45 miles, no train or bus route). Can't afford electric vehicle. Who knows when I will, it certainly isn't high up on my list of worries.
None of this is simple, one size fits all. The only thing one size fits all will, as I said above, be misery either way.