This might be acceptable on average; theory in practice are the same in theory, but in practice they differ. A real-world user will require the ability to fully charge his electrocar on occasion, which means the fullbore 240V connection and a 100A breaker (potentially a 50A breaker depending on vehicle).
Assuming that every user follows average patterns will break the system.
Taking this idea out further, it speaks to infrastructure upgrades that will be necessary in order to power all of these electrocars. Estimates vary by region, power generation from automobiles as a fraction of total is somewhere between 10% and 30%, which exceeds both the spare capacity of the electric grid in aggregate, as well as often exceeding local transmission capabilities.
All-in-all, the costs of electrocar adoption are nonlinear: the first few percent of the population who adopt don't have to deal with the structural problems: a 100-unit condominium building can add two or three 240V chargers, the local grid can handle a handful of vehicles. At scale, however, major infrastructure upgrades will be required.
The other car does 6 miles 3 times a week and is in the driveway almost all the time.
Sure, there are whales that do 300 miles a week, but that's not most people.
Looking at a sample of about 13 million vehicles that passed MOT tests in both 2018 and 2019, and thus reported the milage
Percentiles 20%: 2700 40%: 4800 50%: 6000 60%: 7000 80%: 10500 90%: 14000 95%: 17000
Lets assume that's all commuting over 5 days a week, 47 weeks a year. That means in an average 12 hour night:
20% of cars would need less than 11 miles of charge, or 4kWh -- 350W
Another 20% of cars would need less than 21 miles of charge, or 7kWh -- 600W
Another 20% of cars would need less than 10kWh -- 850W
Another 20% of cars would need less than 15kWh -- 1.25kW
Another 15% of cars would need 24kWh -- 2kW
All of that is less than a kettle, an average 13A plug is more than enough.
Now if those mileages include many people doing long distance drives at weekends and not regular commuting, the actual top-up needed every night isn't anywhere near as much. Some cars will do lots of miles at the weekend and need to draw the full 3kW out of a standard socket, sure. My kettle doesn't have an issue with doing that. For every car needing that full charge on a Sunday and during the rest of the week, there's a dozen that don't. OK, your battery might be down to 10% on Sunday night, but then you charge it to 20% for Monday morning, drop to 17% after your commute, charge to 27% Tuesday, and so on.
100A, or even 60A, house breakers aren't going to have an issue with keeping 95% of cars topped up, so you're at the next level. On the rare occasion you need to fully recharge really quickly, go to a specialist location with a 20kW+ charger. The data shows that most people won't need that most of the time.
Looking at newer cars -- ones made in 2016 (and thus having first MOT in 2019), you'd think they'd have a higher mileage. And they do, median is 8400, and 80%ile is 13,300, 95% 22700 -- about 30% higher in each bracket, but that's still well within a home charge range, even for the 95%ile, and only 1 in 4 cars are new enough to be in that category, so median mileage of all cars would be under 7,000 miles a year range.
You're right there's a grid level problem -- the dip in power generation in the UK overnight is about 10GW, which could sustain about 14 million cars - not too great when there's more than twice that needing power.
Assuming that in a given area cars are distributed fairly evenly as above, with some cars needing 24kWh a night, but others needing 4kWh, the average overnight draw would still only be 700W, that doesn't feel like it's going to trip neighbourhood substations, but further upstream could be problems.