Don Foreman writes:

Yes, that was the original question. But the answer is, regulators are
lossy, even if you assume the compressor is 100 percent efficient and
lossless.

Answer offered is an assertion still dodging the question of where
claimed lost energy might go.

The "assertion" I have fully analyzed several times now. I am not gonna
repeat that.

No dodging. I offered four destinations for the missing energy: friction
at the orifice, sonic noise, turbulence downstream, work done on the
atmosphere by the expansion. Depending on the regulator design, the
proportion of each will vary.