"Triple its staffing" to handle assigned seating?
No way.
I seldom see more than one GA at FL gates - even on full flights
I agree. I have rarely seen a GA bothered with seating changes. Most of their customer service tasks seemed to be centered on telling standbys what their chances are or giving elites upgrades or how late the plane will be or something like that. It is definitely false that staffing is preoccupied with seat assignment changes in the last minute.