Reference FAA-S-8081-4D, Instrument Rating Practical Test Standards, Airplane, Helicopter, Powered Lift:
VI Instrument Approach Procedures (p 1-9 - 1-10)
...Objective...
A. Task Non-Precision Approach...
4. Selects, tunes, and identifies, and confirms the operational status of navigation equipment to be used for the instrument approach.
....
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So you see that it is important enough to be used in the practical test standards and that applies to NDB, VOR, LOC, LDA,....
The question is, if you tune and identify and then turn the volume OFF, how will you confirm the operational status of that equipment during the approach? As long as it is loud enough to identify without impeding other flight functions, that should keep everyone happy.
Specifically required by reg? No, other than the catch-all careless and wreckless operation.