The mayor of a city runs a business meeting, not a speakers' forum. A city government's business is to use financial and human resources to provide services and ensure civil order for residents.
I attend the majority of Costa Mesa's City Council meetings. Recently, a small group of regular speakers has been addressing a new talking point: the venerable 1st Amendment. Their use of 1st Amendment argument is specious at best.
The U.S. Constitution's 1st Amendment guarantees a right to be free from government restrictions on speech, not the right to speak when and where one prefers.
During the meetings I've attended, the majority of the commenters departed soon after making their remarks.
However, those citizens summoned or scheduled to present business matters to the council had to wait while public comment was often extended, sometimes for an hour or more. Hearing an off-key ditty shouldn't take precedence over ruling on right-of-way disputes and infrastructure repair questions.
The new system works like this: Speaker cards are shuffled by the mayor, 10 are drawn randomly by a council member, and the names of those 10 are announced. The mayor allows public comment for the scheduled 30 minutes, three minutes per speaker.
Then the council conducts the city's business, and the rest of the people who want to speak must wait until after the scheduled business is handled. The council members and city staff remain to hear their comments. The process is certainly content-neutral.
Speakers who want to address issues on the agenda can still speak when that agenda item is being discussed. They are limited at that time to speaking about the subject at hand.
It is specious to claim that the 1st Amendment guarantees the speakers the right to speak early so they won't be inconvenienced. TV programming and bus schedules shouldn't trump city business at council meetings.