Devil's Advocate

[Mnyb]

Except that you can hear signals below a noise floor…

Yes 1+ most rooms are much quieter in the midrange low treble where it matters , most domestic noise is in the bass from roads and HVAC

 

[tmtomh]

The OP is only talking about noise. Distortion and noise sound very different (we are sensitive to noise and not really to distortion) and are mostly created by different mechanisms.

The end-to-end multiplication effect you mention is not absolutely correct. Throughout the chain, gain can indeed increase noise and/or distortion, but we also attenuate along the chain, otherwise everything would be always at maximum volume and way too loud. Attenuation done properly reduces noise and distortion. The art of the system is to have exactly the correct amount of gain at the right places with the correct amount of attenuation at the right places to minimise noise and maximise signal.

The OP also clearly mentions distortion too, and his ignoring of the multiplier effect is strongly implied in his claims about gear’s distortion measurements.