i have been getting this white powder (and little crushable white
rocks) coming out of my hot water taps in the whole house - to the
degree that they clog the aerators on the taps.

How old is your water heater?

A bunch of water heaters were manufactured during the 1990's with
a defective component called a "dip tube" that is made of plastic.
As it falls apart, it leaves bits of white grunk in the hot water.

The solution is to replace the dip tube.

--
Andrew Koenig,