Don Foreman writes:

If energy
out = energy in, then there's no net loss at the regulator.

Sez who? The "loss" is in the conversion of some of the useful-energy-in
into waste-heat-out and entropy-out. Whether this waste heat stays in
the regulator to raise its temperature, versus being carried downstream,
doesn't change the fact that the regulator directly caused the waste.

Remember that part of the loss is also in the form of work performed on the
ambient atmosphere, not heat.