Interesting comments --- let me put my oar in.
1- First, typical grid-use has about a 1:10 variance, ie minimum 10% use vs max capacity at peak.
2- Second, typical travel is about 30-40 km/day/car. Use 40 km.
3- Use == 200 Wh/km as avg consumption, around 200Wh/km/Tesla 3, a heavy upmarket car vs a 160 Wh/km on the small economy-bevs, or less on a tiny Renault Twizzy.
So, a typical BEV user needs == 40 km / 200 Wh/km == 8 kWh/day total consumption.
A typical house uses == 20 kWh /day, with the 10:1 variance.
So a house uses about 0.3-0.4 kW avg. load at night, and about 10x that during the peak usage, with an average 1 hour smoothing/variance.
So peaks of 6-10 kW, with avg. 4-6 kW loads per hour for a few hours.
Average typical houses have 12 kW peak capacity, mostly 15 kW+ for newer ones.
Thus, an avg. house at even if at only 10 kW peak capacity, can charge the total 20 kWh into a BEV in about 2 hours, often less than that, and under 3 hours average worst-case.
ALL modern electric grids could, in practice, charge 100% of all our car use, using nighttime electricity, very cheaply, in the aggregate.
A very old house, of only 6 kW peak capacity, could still charge the 20 kWh total in about 3.5-4.5 hours, between 11 pm - 5 am.
Based on the simple fact that our avg. peak capacity is == 12 kW/house or more, but leaves == 11kW+ peak capacity load available during 11 pm - 6 am, mostly at near-zero use.
As-is, where-is, the current grid could support approx 90-100% of electric cars for all users, in the EU, USA, and most-all oeced countries.
It is also extremely cheap, and extremely efficient.
Nighttime power is very much available, very cheap, and even thrown away by the electric utilities via resistor networks.
ANY nighttime BEV income the electric utilities get is more or less free-money to them, since 100% of their costs and investments are paid for by the current system in peaking-power and prime-time power, mostly, about 90%.
Utilities LOVE BEV charging, especially on a variable-load as-available basis, ie BEV charges on an as-available basis.
As more and more wind power is added, and wind power is biased for nighttime, the utilities can turn off more expensive secondary options, and reduce peaking power plants, that are extremely costly.
The costs for utilities go down via BEV nite-time use, incomes go up, utilization rates go up, reliability goes up.
Current systems costs, delivered, zero subsidy, for utilities are about 2-4 cents/kWh, all-in, via 20 year PPUs, in wind and PV.
These drop 5-10% y/y, and already most of the costs, over 50%, are political BOS costs, ie paperwork and political stuff.