TL;DR: Subtracting 3 dB is done to avoid the underprotection that could result from variations in compute the rest of the NRR formula. But some manufacturers incorrectly (intentionally?) do not subtract 3 dB.
The US Code of Federal Regulations - 40CFR PART 211-Product Noise Labeling (mirror) gives the following rationale:
(v) Spectral uncertainty. Possible variation in exposure to the noise spectra in the workplace. (To avoid the underprotection that would result from these variations relative to the assumed ‘‘Pink Noise’’ used to determine
the NRR, an extra three decibel reduction is included when computing
the NRR.)
This is echoed by the The Noise Manual edited by Elliott H. Berger page 429:
The NRR is calculated in a manner analogous to the OB approach, except that
a pink noise spectrum (cqual energy in cach OB) is used instead of the actual
noise spectrum (line | in Table 10.3), the estimated protected A-weighted levels
are subtracted from the C-weighted pink noise and not the A-weighted environmental noise, and an additional spectral safety factor of 3 dB is subtracted. The
spectral factor accounts for errors arising from use of pink noise instead of the
actual noise spectrum to which the wearer is exposed. As in the OB method, the
computation incorporates a 2-SD adjustment for percentage of population protected (i.e., theoretically a 98% protection factor, sometimes explicitly denoted
as NRR4,). The NRR computed for the example in Table 10.3 is 20.7 dB. For the
full computational details of the NRR see EPA (1979) or Berger (1988).
Note that according to https://cleararmor.biz/pages/faq (mirror), some manufacturers "forget" to subtract 3dB:
"We have noticed some companies do not properly follow the ANSI standard and actually list a false NRR value. This happens when companies do not fully understand the standard and fail to deduct 3dB from their test results, which the ANSI standard specifies in section 40CFR PART 211-Product Noise Labeling.
