Ted Edwards writes:

A regulator can be had to regulate arbitrarily close to zero output
pressure and any desired flow. The original uncompressed volume of
air is then released at near-zero pressure. Near-zero pressure times
a finite volume, yields near-zero work. Where did the energy go?

Near-zero isn't zero. Near-zero pressure at finite volume is obtained
from near-zero volume at finite prssure. Where's the problem?

Eh? The final volume of exhaust at ambient pressure is always the same,
namely the volume of free air taken in by the compressor (intook?). You
can regulate the output to as close to zero as you like. Which is to
say, you can take any tank of compressed air and vent it to the
atmosphere, with as close to all of the energy dissipated by the
regulator as you care to choose. In the limit, all of it.

E = Integral P dV

And the limit of E is thus zero as P approaches zero, since V is
independent of P for small P (the compressed volume can only expand to
the original free air volume).

Remember that every expanding container does work against the
atmosphere.

Back a ways you attempted to use a series regulator as an analogy.
This doesn't work since, in a series regulator, Iout ~= Iin and Vout
Vin.

No, Iout = Iin in a 3-terminal regulator, except for a small overhead
that runs the chip itself. Or, model it as a magic variable resistor if
you like.

A switching regulator might be a better analogy: Vin*Iin ~=
Vout*Iout.

Hardly. A switching regulator is just a transformer, with an DC-AC
converter on the input, and AC-DC converter on the output. This would
be analogous to my imaginary "regulator" consisting of an air motor
regenerating the reservoir, not a conventional variable-restriction
regulator.