Another theory is that there are specific class loadouts already selected and you have to pick one, and there's a limit per team.

Alot like America's Army. At the beginning of each game, there was a loadout selection sheet, that already had a predefined number of classes per team (3 riflemen, 1 grenadier, two snipers, two medics)

You had to choose at the very beginning and it was always a rush to see what you would have left by the time everyone chose. However, it was even fun if you didn't get the class you wanted.