If it isn't on the agenda it doesn't happen. If it isn't on the agenda then the room and the time must be scheduled by someone. If the room and the time is scheduled by the government entity that is conducting the meeting then it must be on the agenda.
Nothing comes without unintended consequences.
Here's a scenario that I can easily envision happening:
Beyond contentious topics being on the agenda the public rarely, if ever attends local government meetings and damn near never attends committee meetings. For the most part, without a reporter of some sort attending, local governments and committees could conduct meetings while smeared nekkid in bear grease and the public would be none the wiser. As far as prayer goes I'd venture to say that damn near 95% of the people reading this have no clue as to the history of prayer before local and committee meetings that personally affect them. In truth does prayer really matter in majority of these meetings one way or the other? Hell, no. Nobody goes anyway. No one is really that interested in local government unless it has to do with taxes or the building of a local mosque.
Seating will become an issue in some local government meetings when prayers are held prior to a meeting with hot agenda items. Seating could well become political as those not wishing to hear the prayer wait outside the meeting room until the prayer is completed. Prayer listeners go in first and get the best seats. When the meeting agenda contains a hot topic the meeting will likely be SRO. Those who don't want to hear the prayer get the worst seats or no seats at all. This will become an issue unless people are permitted to enter before the prayer and reserve their seats. At contentious meetings even seat saving may become nasty.
If the hot topic on the agenda happens to be one that attracts religious extremists block seating will become a political issue. Count on that.