[tomn]

> They have to be loud enough to be heard through hearing protection.

It's kind of a nit-pick, but this is not really true.

Very approximately, you will perceive a sound if it is above your threshold of hearing, and also not masked by other sounds.

If you're wearing the best ear defenders which attenuate all sounds by about 30dB, and you assume your threshold of hearing is 10dBSPL (conservative), any sound above 40dBSPL is above the threshold of hearing. That's the level of a quiet conversation.

And because your ear defenders attenuate all sounds, masking is not really affected -- the sounds which would be masking the reversing beepers are also quieter.

There are nuances of course (hearing damage, and all the complicated effects that wearing ear defenders cause), but none of them are to the point that loud reversing noises are required because of hearing protection -- they are required to be heard over all the other loud noises on a construction site.

> The utility of having a backup beeper or any noise making device on that site is thus zero.

The inverse square law says otherwise; on site the distances will be much more apparent.