From the moment it was said that Übel was disqualified for killing a Proctor mage (possibly as revenge since she kills in self-defense), I got the feeling that they didn't outright banish her because they wanted as many skilled mages to attend and dying in the First-class test, either as a means of mage population control to keep the existing elite mages at the top or to prevent mages from becoming a threat against normal people without talent for magic in a post-Demon Lord era.
This mage class bureaucracy nonsense serves no practical purpose. It's just a bloodsport that'll give Demons an edge at the end of the day.