Gary Coffman writes:

Power is not a conservative quantity. Energy is, and the energy not
released is retained in the tank. In other words, power = energy/time.

Your statement is contradictory, although I think I understand what you
mean. Power can be converted to heat and thus not "conserved". I
suppose what I should say is that the power going into the regulator
either comes out the other side, or is lost as heat.

This ends up as heat as a direct consequence of the restriction that
creates turbulence and lowers the pressure. This waste heat is mostly
added to the output flow, even though the output may be at a cooler
temperature due to expansion. Some of the power lost is hissing noise
that radiates away and also eventually becomes heat. None of this is
"visible" to the source, so it is not "simply retained in the tank".

Those parasitic losses are relatively negligible in a well designed
system.

I don't know what you mean by "parasitic" here. Regulators are
inherently inefficient devices, and part of the input power is always
wasted (ultimately) as waste heat by them.

Think of the case where you have a "perfect" regulator lowering the
input pressure to ambient pressure (0 psig). For example, imagine a
pressurized tank that you instantly crack open in half. Or for a better
imaginary example, imagine that you have a compressed tank, and you can
magically make the tank disappear instantly, leaving the mass of
compressed air suddenly unconfined. Where did the power go? You get a
noisy bang, and a lot of turbulence, which ultimately degrades into heat
equal to all the energy previously stored in that compressed air.

Similar puzzle: shorting a perfect capacitor with a perfect conductor.
Where does the energy go?