"If you want to improve the efficiency of the water heater, then you
insulate these pipes. More than that much would not be useful, as the
from the water heater is lost in the first few feet of copper pipe.
will also reduce by a couple of seconds how long you wait for hot water
when you turn on the tap. "
So, the water is back to ambient temp after running through the first
few feet of pipe? If that were the case, you'd never get hot water.
And it isn't going to make hot water show up any faster, except in the
case where it's reused within a reasonably short period, before it
cools off again. But, for example, first thing in the morning, it's
still going to take just about the same amount of time to get hot water
with or without insulation.