Gary Coffman writes:

Power doesn't go anywhere. It is a *rate*, not an actual thing that
moves.

You make a contemptibly false statement, ignorant of even high school
physics.

Consider an three-terminal electronic constant-voltage regulator as an
analogy to an air regulator. Say you input 7 volts DC at 1 amp to that
regulator, while drawing 5 volts at 1 amp out. The input is 7 watts of
POWER and the output is 5 watts of POWER. Yes, the POWER moves through
the device, an "actual thing that moves" as much as anything in physics.
The difference of 2 watts will be dissipated as waste heat in the
regulator device. In an air system, CFM is analgous to electric
current, and air pressure to electric potential (voltage).

Some amount of energy is stored in the tank, some lesser amount
comes out through the regulator valve as a mass flow. The rest remains
in the tank until used at some later time.

Absurd. If you run a given mass flow of air (CFM) at a higher pressure
into a regulator, and draw the same mass flow out the other side
(necessary by mass conversion), at a lower pressure, then the difference
in pressure times the flow rate (CFM) represents the the power being
lost in the regulator. The more the drop in pressure across the
regulator, the more the inefficiency.

In the extreme, you can make a device that will "regulate" compressed
air to output an arbitrarily large flow at an arbitrarily small
pressure, and dissipate all of the energy in the tank in the regulator
itself, such as diffuser device.

It is stupid to think that the difference across a regulator is somehow
"retained in the tank". You can continue the regulated flow until the
tank is empty, and then you have nothing in the tank. Depending on the
regulated pressure drop, you can do more or less work with the same flow
of air. The difference is wasted.

In general, regulation of *any power source* implies an inherent waste
versus the unregulated source: electrical power, compressed air power,
motive power, water behind a dam, etc.

So, if you draw 1 gallon of water a minute through a valve at the base
of a dam, the other 999,999,999,999,999 gallons in the reservoir are
wasted. Obviously not true at all. You use what you use, the rest
stays in the reservoir (with all of its potential energy intact) until
you need it.

No, the analogy here would be regulating the head behind a hydraulic
dam, by allowing the excess to flow over a spillway. The spillway flow
performs the head regulation, but only at the expense of wasting the
power (or energy, if integrated over time) available from the water
"over the dam". Such wastes are inherent in any regulation scheme.