Don Foreman writes:

That's where the energy goes: out the exhaust port as
heat energy unavailable for doing useful work. It is NOT lost in
the regulator,

Not necessarily. A braked turbine is one way to build a regulator. You
could regulate down and take off some of that work at the same time, and
less heat would go out the exhaust.

I repeat that "lossy" means "attributable to the device", whether or not
the device itself gains the waste heat. This was to refute the original
these of this thread that regulators were not lossy.