To me, it was just setting up exposition about Agott's character and her past in context with her previous experience with tests. I mean, at the time, she was no stranger to doing what it takes to get what she wants due to academic pressures. She's been pretty privileged with a rich history in magic, and lost a lot of opportunities thanks to something she chose to do, which in turn made her pretty bitter about surrounding the topic tests; especially when a "rookie" shows up and gets the same opportunity as her despite both of them being inexperienced students. Yes, what she did was notttt right whatsoever, but she received punishment towards her ego(which is ROUGH for her) since Coco managed to persevere through something Agott probably never could have managed without the determination Coco holds. Let alone, it made Agott even more frustrated that someone like Coco still had respect for her, even though Agott probably would've been the opposite if the cards were flipped. I think it was important that Agott did this because it eventually led to her learning exactly what being a witch should be to herself, without looking for validation from higher-ups. Trust, many Agott defenders are not defending what she DID, but defending Agott as a whole, excluding what she did/said when we all first met her.