Could you attach a pound, dollar or Euro sign to the work your function does? Should you even be expected to do so? Or is to ask the point of spending money on communication and engagement to entirely miss the point?
I’d suggest that whilst it might be hard/impossible/unnecessary to prove the case, depending on your viewpoint, the cost of doing nothing, of ceasing all communication is clear enough for everyone to see.
If empirical evidence, or old-fashioned commonsense isn’t enough, disconnect the phone, take away the PCs, shutdown the channels, ban conversation and see what happens.
Or do the human capitalists have an Excel that makes the point in a more sophisticated and credible way?