If members of your council find “open discussion difficult” there are probably greater potential problems than whether, or not, the apparently “connected” councillor stays or leaves the room.
What “connection” is it supposed that they have? Are they the applicant, the land owner or related to someone who is? What is the “connection?”
What do you define as “open discussion?” Is what you really mean subjective “opinion?”
Open discussion (of relevant planning factors) should be the cause of no concern to anyone that has objective reference to appropriate planning considerations. If it is subjective opinion then it should be noted as inappropriate anyway - regardless of whether the “connected councillor is present or not.
Whereas model orders “suggests” a councillor should leave the room if an interest is declared, it is patently obvious - and illustrated by the observation within the OP - that this is a doubly pointless exercise since any ally of the person leaving the room may remain, record and or video the exact part of the discussion, and, that part of the meeting may be livestream broadcast or recorded thus providing the temporarily absent individual the opportunity to review proceedings anyway.
Applied intelligence therefore makes it patently pointless, disruptive and disjointed to insist a person leaves a part of a meeting which they can view / hear later anyway.
Model orders are a “suggested” model not a mandated one if the people making the suggestions haven’t kept pace with practical changes then their suggestions don’t have to be adopted