If the average EV gets 3.5 miles/kWh, then those 20 miles per day need ~6 kWh. That's 600 kWh a night for your 100 cars, which over 10 hours is about 60 kW.
That's far more achievable - comparable to 5 houses using an electric shower at the same time.
There's bound to be some localised challenges, but the amount of electricity required for charging is well within most grid's existing capabilities. Grids are built for peak demand, with the low usage overnight typically half of peak. Additionally, electricity usage per household has been falling in the west for the last decade - with a peak in the mid 00s. The energy efficiency savings in lightbulbs and appliances have given extra headroom for charging.
The average car in the US drives 14k miles a year. At 3.5 miles per kWh that's 4000 kWh a year, or an average of 460W. The average US home uses about 10,000 kWh a year - so that car charging represents a 40% increase. As long as that 40% is in the night, when infrastructure is barely being used, it's not really a problem.