Being a commoner, hated by most student, just technically a freshman, and know nothing about them personally but this cliche loli principal tasked her to a task that sounded like what the teacher should resolve, huh?
She said she is "the most reliable" when she herself is just a freshman in the academy and being hated by most of the student.
This task seems to require a number of connection, and most importantly trust from the student involved, which being a freshman and hated by most student seems to be really contradicting.
Another possible way is just to complete all the unresolved quest, which I guess would be a lot and just asking a freshman to do something like this is like clinging to faith. They do know her performance in team but alone? While being at a disadvantage cause of "no family insignia" as a form of reference? How would she even accept all the quest properly? Isn't sending a 1st year scholar to any 3rd year student quest feels like a suicide mission?
Also, if the 2nd and 3rd year are failling, why ask a 1st year freshman to do all the work without prior background and past performance check? Just cause she is scholarship student? Cause she had big magic number?
Yes this is not impossible, but it's too hopeful to place a big bet on a 1st year commoner freshman with no family insignia and no past performance log. At least task her to form a team to ensure she is not alone in this task.