I just started my second city a few days ago and it does not have barracks!A pure caterer will struggle at the very top of leader boards but is otherwise totally viable. BUT it will probably have a barracks and win things like Dwarven armorers that go to waste.
In my origin city, that was something I was told to place, as are many things as it guides you through getting started. But I later discovered that as a caterer, the barracks were worthless. That's one thing, but the real disappointment is discovering they are one of only a few non-sellable buildings, so serious waste of space.
And, yes, I'm tired of getting DAs in the Spire. Coveted by many but useless to me.
[edit: leader boards are the last thing I care about so, though viable, I'm not even trying to climb the board.
My comment was more toward barracks and DA.]