I'm a homeowner with a home charger. When I get home I plug in. It doesn't usually start charging until way late in the evening. Currently it's just on a timing schedule I set up once, but soon it'll be linked to my electric provider to automatically shift to whatever is an off-peak time for them and I'll get a discount on my bill. In the end I can still tell it to just go ahead and charge but typically it's going to sit there overnight and I can normally go a few days between charges anyways.
Pretty much every recent model EV can do this on its own. Many EVSEs (Electric Vehicle Supply Equipment, the "charger") that have any level of smarts can also do this. My EVSE is just a dumb one, it just tells the car it's capabilities and it's up to the car to choose when to charge.
Adding an EV to my house didn't change my peak usage at all.
