> but what's stopping the power/timing controls from being buttons on the charger wall unit?

The car makes all the decisions about how much power to draw and when to do it. Excluding the DC super/fast chargers, the hardware on the wall is pretty "dumb".

It's been pointed out elsewhere, but remote notifications are useful so you know it's time to get out of the public charger and let somebody else in (or to go back out and check on why it's suddenly stopped charging)