Gary Coffman writes:

It isn't the regulator which is wasteful. The energy loss is in the
compressor you're asking to pump to a higher tank pressure. And no
surprise, it is the compressor which gets hot as it does so. *That's*
where the energy loss in your scenario occurs, not in the regulator.

No. The compressor can be assumed perfect.

THE MAXIMUM ATTAINABLE WORK DOWNSTREAM OF A RESTRICTION IS NECESSARILY
LESS THAN UPSTREAM OF THAT RESTRICTION.

The operating principle of a conventional regulator is a restriction.
It is just a valve with a feedback arrangement on the handle
Restrictions are lossy. Otherwise we'd be using the thinnest possible
air hoses instead of paying for big ones.

The regulator itself has nearly zero loss, as my example of drawing
down a filled tank to supply a load shows.

I've lost track of who is exhibiting what. But this waving of hands
with Boyle's law and energy being P*V is flawed analysis. It shouldn't
even take analysis. It should be obvious, anything that impedes the
flow of compressed air has got to be robbing power.