I’m so old remember when opponents were respectful and followed the rules. It is too has that a certain person forced this type of action.
To answer your question, Yes!
I would make 3 changes:
1) A timer should automatically mute the non-speaking participant. The muting should be automatic so no one can claim the moderator is biased.
2) If the non-speaking participant makes noise in any way, such as: huffing, pounding the table, booing, name calling, etc. a red light will flash on their console to indicate the infraction. Their rebuttal time will be reduced by 10 seconds for each infraction.
3) The cameras should only show the speaking participant and ignore the opponent.
All of the above actions can be performed automatically. (I’ll make the system that does it if they cannot find a source.).
I’d like to add a 4th rule that penalizes opponents for unmannerly actions such as: name calling, cursing, temper tantrums, immature antics but that would require a moderator with backbone and would bring in the question of bias.