The power grid is built to handle peak demand. Residential charging is likely to peak at night, when domestic demand is at its lowest.

If natural charging patterns are not advantageous enough it's fairly straight forward to install smart meters that charge a different electricity price depending on time of day. The options range from simple off-peak pricing already offered in many places all the way up to live updating prices based on electricity spot prices and transmission capacity (this would also go a long way towards using solar and wind more efficiently).

The big problems are likely shops offering EV charging and industrial facilities with fairly constant power requirements charging trucks and heavy equipment. But those are comparatively easy to scale.