This is where having a level 2 charger at home, even if the car sits outside is a real benefit.
Level 2 is not needed for most EV's to warm the pack. Yes its quicker and nice to have, just not needed.
Of course if they don't have the means to plug in at home( or have to rely on 120V charging*), an EV is not for them right now.
*Rely on 120 and live where it gets cold. If live in a warm climate, 120V can be fine. But in the winter, 120V does not supply enough power to charge the battery, warm the car, and warm the battery.
You are correct in thinking that it doesn't directly supply enough to charge and heat at the same time. But the car's battery management system will figure it out and you CAN leave in the morning with a 100% battery and fully heated battery on a 110v level 1, it just takes longer.