This is old technology, I'm surprised the US hasn't already implemented it. They have been remote-controlling water heaters in New Zealand and Australia since the 50s. Just a simple relay installed in each house that responses to extra frequencies on the power lines in the 160-1600hz range. It's called ripple control, for obvious reasons. Each home gets assigned to one of several channels in each area so they can hav…
About half of the US uses natural gas for water heating - its substantially more efficient than burning said gas (or coal) to generate electricity, then using the electricity to heat water.
While this is true for basic resistive electric water heaters it's not for modern heat pump water heater which have energy factors of 3.5x which more then makes up for the 34% efficiency of a simple gas power plant (more modern combined cycle plants are 50-60% efficient) and the 95% efficiency of the grid.
Still works out much cheaper to use gas than electricity for heating in California with gas at $0.06/kWh vs $0.26/kWh for electricity.