If you have enough 3-6kw chargers for everyone who wants to use one that stops being an issue. If a percentage of the cars are plugged in but done charging, that just means you can get away with a smaller grid connection and load share across the chargers.
I'm Not An Electrician, But ... The wiring to hook up 50 or 100 L2 3kw chargers is so much more $$ than just running for 12amp 120V service. The cost in thicker copper & insulation alone is way higher.
If I'm parked for 8 hours at work (thank god I now WFH though...) depending on the car & weather, etc. I could get 30-40km of charge for my Volt just from an L1 hookup. Most people's commutes are less than that.
(Where I grew up in Edmonton, Alberta it used to be fairly common to wire staff parking lots up with 120v lines for people to plug in their block heaters for extremely cold days. Granted, in that case there was not continuous service -- just rotating or intermittent or whatever -- because you didn't need a full charge all day to give heat. Newer cars don't really require this, they start more reliably.)
It would certainly be better than nothing. One thing is that requires everyone to carry their own mobile EVSE with them. Not every car comes with a 120V EVSE included these days.
Also especially in cold weather the charging efficiency can be very low. Energy is needed to run the car and BMS systems, and to condition the battery temperature. With a 240v charge a higher percentage of that input energy is actually making it into the battery.
The wiring isn't necessarily more expensive either.
120V * 12A = ~1.4kW. Wiring here is 12awg or 14awg, 1 hot, 1 neutral, 1 ground.
240V * 12A = ~2.8kW. Same amps so same wire size. 2 hots, 1 ground.
If you go with 12awg I think that's actually rated for 16A continuous which would give you ~3.8kW
Yeah, charging at 120V 12A when it's minus 20 barely budges the needle. OTOH the battery is warm when you leave, so your drive home uses a lot less energy. Doesn't quite balance, but it helps a lot.