Think of it like this. Obviously, City's primary argument will be that the audited accounts show that everything's been done legitimately and that should be regarded as conclusive. However, you can't guarantee that they'll accept that argument - one member of the CAS panel didn't, for instance - so you have to be meticulous in devising as many reasons as possible to chip away at the other side's evidence to give the IC as many reasons as possible to doubt the PL's case.
It's highly unlikely that any of the PL's emails that are produced will be blatantly incriminating in terms of member clubs and PL executives conspoiring to screw us over. However, I'd argue that any contact on the subject is inappropriate and I suspect there will be exchanges that allow City's lawyers to portray the PL as coming under pressure from influential clubs to act against City. That can be used to create further doubt in the mind of the Panel.