Fortunately those "clothes dryers" are already connected to the internet, and have sophisticated power electronics hooked to the grid that can detect voltage sag and phase lag. Connected to a central server, each car (or stationary battery, for that matter) becomes BOTH a sensor that can monitor grid health AND a remote-control load that can be dialed up and down (so long as the car gets a full charge before 7am, or whenever the user chooses).
The internet allows entire neighborhoods of EVs to be controlled at once, so that the substation is at 100% power and no more, and so the distribution/transmission lines are at 100% power and no more.
Is that a hard control problem? Sure. BUT it's easier than overbuilding the electric grid by 2-3x (which is, after all, the largest machine ever built[1]). And given the very large opportunity cost, there's a lot of incentive to solve it.
[1] https://www.smithsonianmag.com/videos/category/innovation/th...
With off-peak rates and people having different schedules(I'm home at 4pm for instance) I don't see why everyone would be hammering the grid at 5pm.
Of course as has been pointed out repeatedly a smart charger can manage exactly when the battery starts to charge. However it isn't quite that simple: many of those people will go out again for their bowling league or whatever, and need enough charge in their car.
Los Angeles and parts of the Bay Area have had nearly annual brownouts for the last 20 years just from air conditioners during heat waves. How in the world do you expect that aging power grid (in the fifth/sixth largest economy no less...) to handle a clothes dryers in every house running 4+ hours a day?