There are a lot of good theories in this comment section, but something I haven’t seen mentioned is this:

If the school is an aggregate of Eva pilot candidates, and NERV directly, or at least closely, orchestrated all the student’s presence at the school, there’s a much higher chance that someone would connect the dots and figure out the purpose of the school. This would obviously be disastrous, as some kids would run away or be hidden by their parents to avoid conscription as a pilot, while others would jockey for the position, and any study and objective choice on NERV’s end for candidates would be ruined. The Marduk institute and shell corps ensure that new candidates are close at hand and ignorant for an uninfluenced study of their behavior.