The “obvious way to handle this” is to build cities without cars at all, where people walk and bike and take the buses and trains.
This is very misleading. It takes several minutes to fill a gas tank (depending on tank size, pump speed, and how many times the damn thing gets gaslocked). Charging a modern BEV does not take several hundred minutes. Fast charging exists and functions similarly for BEVs as it does for cell phones - fast charge for the middle bulk of the cycle, charge rate slows to a trickle above 80%.
Chargers generally cost per minute, so you're incentivised to stay plugged in for the bulk fast-charge portion of your charge, not the trickle at the end.
At a much more common 6.6kW charge station you're getting 25 miles per hour of charge. I can put about 350 miles of gas in my car in one minute.
It's a bit unrealistic to expect people to park again after the charging is done.