Harry K wrote:

wrote:

...a well sealed insulation jacket will not allow
moisture to fomr on the pipe.

And it may increase the water heating bill.

Not in any measurable way...

I disagree...

Care to expound on why? The amount of water contained in a 3/4" pipe
say 20 ft long is not very much. About 5 cu in/ft...

I get 0.19 lb/ft, so 20' would hold 3.8 pounds.

...Water in the cold intake pipe also doesn't usually sit there long enough
to pick up much ambient heat.

That depends on how fast the heat flows... 20' of 3/4" pipe has about
4 ft^2 of surface. With still air and no condensation, it might have
a thermal conductance G = 1.5x4 = 6 Btu/h-F, so the time constant RC
= C/G = 1 hour, ie a 3.8 lb slug of water would warm from 50 to about
57 F (1/e th of the way to 70) in 1 hour in a 70 F room.

Recall Charlie Wing's TV show in which he built a tempering tank in
a basement, a 20' length of 6" PVC pipe tucked up under the rafters?
Well pressure tanks can warm water too.

And condensation might raise G to 1000, so flowing water can warm to
the dew point in real time as it moves along the pipe. As I recall,
the OP described "a few feet" of condensation near the pipe entrance.
I don't recall that the entire pipe had condensation when water was
flowing. If not, the pipe warmed flowing cold water to the dew point.

With no cold water pipe insulation, we have 4 potential savings in
water heating: the small warm slug of still water before flow begins,
the large flowing gain to the dew point, the small flowing gain from
the dew point to room air, and the effect of having warmer cold water
at a sink or a shower, which can allow using less hot water in a mix
to achieve a certain temperature. The latter may come from a lot more
cold water pipe in the house, unrelated to the pipe that goes into
the water heater. Harvard physicist William Shurcliff has written
about these savings.

Nick