The grid has a "duck curve", which means there is a lot of spare capacity outside of peak hours. And moving EV charging out of the peak hours is doable.

Many charging stations already have batteries on site, because it lets them use cheaper electricity and/or provide charging speeds faster than their grid connection.

EVs used for commuting are very flexible with their charging times. They can automatically delay/schedule charge times. Median US commute (35mi) requires charging about once a week. People who can't charge at home could charge at work (such low-speed chargers are relatively cheap and easy to install).