It's inappropriate because it's not a criminal trial, the "evidence", as it is, is not presented to prove someone's guilt to a criminal standard.
The terms of reference of the inquiry is to determine how a serial murderer managed to get away with multiple killings right under the noses of hospital staff and management and how these things might be prevented in future. The foundation of the whole inquiry is that LL is guilty - as the courts have properly determined her to be.
It's not appropriate to pick apart specific bits of the evidence because, for a start, its admissibility is not to the criminal standard because it's not a trial. It's not even a civil trial which has looser rules of evidence and a lower burden of proof. The inquiry is looking at how the hospital and its management behaved, not whether she is guilty. That has already been decided.
They are looking at how the Trust behaved, not LL. The evidence and statements given by the witnesses need only be of a general nature and they won't be getting torn apart as a barrister would do in a criminal trial.