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Yurisivel: The thing is, the majority of the Knight's didn't really know or understand what she did, so her breaking some of the Knights Chivalry isn't really a problem.
And, from the way the story is presented, i think this story is trying to focus more on the negatives of Knights Chivalry, with their unless notions of stuff and prestige that don't have any meaning. Especially Fia's brothers who keep looking at others weaker than them with contempt.
As for her training, it was already said that Fia didn't even have a little bit of talent with Swords, so whatever training or hardship she did was mostly wasted or atleast only made her reach basic level of proficiency.
People are good at either one thing or another, while also being bad at one thing or another. Just because she failed and used Magic as a support to achieve her dream isn't really wrong as even her Magic is her own strength and ability. So, Fia cheating isn't really a terrible moral message, because the cheats she used is also her own powers, rather than external factors. What Fia did was simply use her abilities she is good at and used her brain, which isn't bad. Remember, there isn't much difference between a Knight and a Magic Knight.
Fia isn't really the underdog though. Its obvious that she is weaker at Swordsmanship and base physical strength, but she was a Saintess in the past, and gained back the base mana capacity she had in her past life. So, at base she is practically one of the strongest beings alive.
As for why she was trying to avoid her brother, and even tried to gain a default pass, was because what she wanted to become was a Knight anyway possible (originally, she wanted to become a Knight so that she could prove herself to her family, but after recovering her past-life memory, she kind of forgot that notion, and aimed for Knighthood, as a different path of work). So, just because she tried to gain a pass on her test without doing much isn't that big of a problem, as people in real life also do that.
Plus it was her brother who was the tester whom she wanted to avoid, because they had never treated her properly until now, and it was possible that the brothers would have been extra hard on her (if she didn't use magic boost), and probably beaten her more badly compared to others just so that they could prove their superiority. In a situation like this, anyone would want to skip a test and go for default pass.