No one wanted to become a joke, not in front of the whole army! Otherwise, the nicknames would never disappear, and they would only suffer.
Even if the whole army suffered the same fate, it made no difference at all, as they would still have experienced something like this and they wouldn't be able to forget it.
But most importantly they needed to relieve their anger and their stress on the people that were responsible for the matter.
Perhaps if their counterparts had shown a bit of understanding things wouldn't have escalated that far, but their counterparts were suffering for themselves.
They had no reason to eat shit from some bastards that came to their doors, when they were in the same position themselves.
For that reason, confrontations soon turned out in fights among individuals, and after that groups got involved, bigger groups followed, and soon it looked like the whole army.