The main reason why Aaron showed his power in the alliance exam was to get access to certain information that others couldn't access.
While in school, the students were taught a few things, but much of the information was kept a secret from them. Some of that information would only be accessed when they attend the academies.
How much they can access depends on the academy that they attended.
The top five academies have higher access to the information of the world when compared to other academies.
This is why Aaron decided to show his power. He wanted a seat in the top five academies.
Moreover, most of the knowledge about the professions could only be accessed in the academies. As the academy that favors Dark and Death professionals, if he wanted to understand his profession to the maximum, he needed access to the library of the Dusk Academy.