Having such prayers can lead to so much hypocrisy. In the city where I live, they decided to keep the opening prayers, but when an imam was scheduled to say the prayer some of the city council members and congregation waited for him to finish before they entered the room.
In the city where my synagogue is, both my synagogue and a nearby Hindu temple were not allowed to participate because the Christians in the city council said that it made them uncomfortable. The following year, when they were told that we were going to file a lawsuit, suddenly they decided that maybe inclusion wouldn't be such a bad idea after all.
And not too far from my place in the U.P., the board of education in the nearby town wouldn't allow the Ojibwe there to have after-school drumming, and yet they allowed after-school Christian gatherings. The township council told the board that either they had to include both or exclude both, and the board decided on the former.