Why is there insulation in the common wall between housing units?
The first 3 comments are all correct answers.
Comment #1 by ThreePhaseEel regarding a code required fire wall is correct, but it’s for fire rated draftstops between living units.
Comment #2 by Isherwood regarding sound control is also correct. The code requires a minimum STC rating between units and insulation can fill the voids and help with that requirement.
Comment #3 by whatsisname regarding a thermal barrier is also a code requirement. The requirement is for the envelope around a unit...there is no exception for common party walls.
Do not remove the insulation just to extend some cables from your attic to the other floors.