±2dBA would already be much more precise than what you'd need to assess if a certain sound pressure level can be endured for an extended period of time safely, or not.
To put it in numbers: ±3dB is doubling/halving of Power, but humans typically perceive a change of ±10dB as doubling/halving of "Volume". Also the damaging effects of noise typically scale as double-the-power, half-the time.
And personally I'd rather not be in the situation where I'd ponder if the damage to my hearing is double or half what it should be if my iPhone app were accurate: I'd rather have it show numbers that are 20dB below this level, so that I can be assured of no significant damage at all!
To put it in numbers: ±3dB is doubling/halving of Power, but humans typically perceive a change of ±10dB as doubling/halving of "Volume". Also the damaging effects of noise typically scale as double-the-power, half-the time.
And personally I'd rather not be in the situation where I'd ponder if the damage to my hearing is double or half what it should be if my iPhone app were accurate: I'd rather have it show numbers that are 20dB below this level, so that I can be assured of no significant damage at all!