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.
The big question is how you deal with the peaks. Ideally all cars would be able to charge overnight, so you could potentially spread that demand over 12 hours or more.
https://www.engineering.com/ElectronicsDesign/ElectronicsDes...
What about the charging infrastructure itself?
The first point in particular doesn't seem to get the attention it deserves.
As an example some places (try to) ban crypto mining because the extra power load effectively makes power more expensive for everyone.
The residential grid is built with a particular established demand for power. EV charging would significantly change that in many places.