Instead of noise, maybe use your own custom sample like a 50hz humming to emulate bad cabeling.
If you want to go complicated you could listen to a frequency range but generate noise to another frequency range (e.g. Use the input of the low end of a kickdrum to create noise in in the higher frequency range), like an internal side chain.
There was a plugin many years ago called mb envelope (or something) that did exactly this but the inbuilt envelope follower was very unresponsive, it gave short instruments like hihats too much of a tail.
I know similar results could be achieved by routing in your DAW, except the envelope follower part.
Just an idea..
