this is more a general response,

one thing that is heavily implied throughout the series is that pretty much everything the Aes Sedai do in modern times either stems directly or is a secondary effect of the breaking and then probably solidified by the trolloc wars.

from simple things like determining rank by strength in the power (when people are dying all around, there isn't time to figure out who deserves to be in charge, and women can easily tell their relative strength) to being able to call a meeting of the hall without having everyone present (jane's out on the town, we can't wait for her to get back so we can decide how to stop the evil trollocs!).

i would venture to guess that this whole 'sit down in the order we came in' thing is more of the same.
they probably did just that-- sat down however they got there with the most senior getting preference.
remember also that in the AoL, ajahs were not fixed the way they are in the third age. i would guess they never bothered differentiating back then as much as they do now.
anyway, when things calmed down and everything was relaxed, they never really bothered to change the method they chose their seats, instead changing the seats themselves.
it's a little goofy, but it fits in with a lot of the other somewhat goofy traditions in the tower.

edit: it's also important to remember that the Tower indoctrination plays a big part on why things like that never change. Aes Sedai are taught to never go against the grain-- to never question the Tower and only young women, who haven't learned to question things on their own yet, are accepted.
it's a mindset that sort of fed on itself preserving practices that were outdated.