If they've done their jobs and confirmed that I have no weapons, and I've been identified (once, discreetly), there's no reason why the face needs to be kept on display throughout the visit.
You are incorrect. There are numerous occasions in which members of the public gallery have shouted obscenities/jumped down into the chamber/caused a ruckus. It happens often. If security guards in the public gallery are not able to identify the offender--and it is impossible to identify the offender if the face is covered--they cannot then take action; ie, remove that person.
Federal Parliament is not like a military base.