Input inductance is very relevant to sound.
For example it can compensate or not for the proximity effect, Fletcher Manson brain perception curves, Voice effort curves of human voice and singing production.
How impedance varies with frequency is important.
Perhaps the best is having both specifications. Or even more. For example what is the input impedance, what is the input inductance, how does impedance vary with frequency, what is the equivalent input noise resistance etc.
As an example of the above elements. One pre preamplifier can have 3 200ohm rated inputs. One with 1 Henry input inductance for orchestral applications, one with 300mH input inductance for voice or singing. And one with 140mH for close mic singng, compensating the proximity effect etc.
Input inductance depends on the number of turns of a coil in parallel with the input signal. It may be a Pleiades filter or the primary inductance of the input transformer etc.
These considerations may be important as what matters is not flat frequency response from mic to loudspeaker. But flat frequency response from producer's brain to listener's brain.
Reference:
Flat frequency response from actor's, singer's brain to listener's brain, Sound picture recording and reproducing characteristics - Loye, Morgan - Journal of the Motion Picture Sound Engineers
Coil Design and Cinstruction Manual - B.B. Babani
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