California has been asking people to reduce electrical use for decades, well before EVs. This isn't an EV-induced problem. They obviously aren't helping, but let's not pretend California's power grid was doing just great before EVs came along.
The Tesla video is from Thanksgiving a few years back, and is definitely not the norm. Most people charge at home.
Mine charges at 6.6 kw. I have it on a 50 amp breaker and my charger supports up to 9.6 kw if I ever get a car that supports that higher rate. The battery is 60 kwh, so a 0-100% charge takes about 9-10 hours, but in reality it only takes me about 10 seconds to plug it in when I get home and another 10 seconds to unplug it when I leave the next day. It's not like I have to stand next to the charger while it charges like one does at a gas pump.
I've averaged 3.6 miles per kwh over the life of the car. Meaning, if I drive 100 miles a day, my utility bill will increase by 28 kwh + the roughly 10% efficiency loss, so call it 31 kwh to drive 100 miles.