This lip service was something realized by everyone else as they knew that claims and reality were vastly different. It was one thing to say the mage division was open to everyone but someone actually tries out for it. They go about seeing what the division is really like then they must either give up unable to handle the reality or accept it and then work towards climbing up the ranks. Doing anything as long as it's within the confines of Valia's system and the creed is followed. Anything goes as long as it does not harm Valia and the image of the mage. Somehow this system had been working as intended since the founding of Valia without problems....or without problems that are not solved rather quickly.
What seemingly no one of current Valia knew was the survival of the fitness setup, the one that was set up by the founders of it. Were originally usurpers themselves(something they ensured was not written down in history) made so that everyone was loyal to the country they created. They were not so loyal to each other, thus making it so they could not band together against them. It was not an easy thing to set up but once they had done so it was done in a manner where it did not harm the country's fighting force when it was needed the most. Also, keep out those who might attempt to change it from within. This would have been a problem if all the other countries around them had not also done something similar. That being creating a country in their own image and desire but those a stories for a different time and place.
However despite the best intentions and planning there were times that ended up leading to the case like with Lutz. Who was considered to be someone that was not deemed worthy enough to become a Mage of Valia. He might have had the raw talent but the mage academy was not the place for him to learn how to use that talent. It was meant for those who already knew and refined it to further do so but compete against everyone else. Get better and advance through the ranks by beating everyone else around you.
Allowing Lutz to remain and continue to take the exam without ever figuring out that he will never succeed because he was never meant to. That someone everyone else but him understood after a few tries. That the exam was created in a certain way to attract a certain crowd and you could either adapt to match them or leave. Lutz was unknowingly creating a third option and that could not stand as no one else was doing what he was doing at least not yet. So to nip a problem in the bud before it got even developed or even worse more people started being like Lutz. More people than being more that started to constantly fail and rather than keep trying as he had they would question the overall system.
A limit to the number of tries that one could take to become a mage recruit for the mage division was placed. Thus anyone who passed this limit was not allowed to take the exam anymore, thus keeping the image that the mage division was open to everyone still. The image would remain the same as it always had as the limit would not harm since the blame would be placed on the person. After all, they were allowed to try out and failed to the point where the general public would see them as the problem. After all the mage division was open for all to try out and if they met the requirements then they could join the division.
Using the exam and academy as the first filters to drain away those that did not meet the actual requirement were the purposes of those two things. Someone like Lutz coming along was an unexpected factor that they could not address properly until they fully realized it. One can not get an answer to a question they did not know needed asking in the first place. So the delay in dealing with Lutz was the result of such a thing happening. However in the majority of these cases once the question was indeed realized coming up with the answer could be almost too easy and/or simple to intact going forward. Just because a question is unknown does not mean the answer to it would be hard to do and/or carry out. The biggest issue is not the how or the why but the what instead. Once you know what you are dealing with then that is when all the other pieces can fall into place and that is when it can be discovered if obtaining the answer is easy or hard.
Anyway, those of Valia learn what they had to do in order to not just get rid of Lutz but prevent anyone else from repeating what he had done. It was quite simple to do so the next step though was just to ensure that they did not have to deal with the origin of the problem again. They got rid of Lutz by not just sending him to a nearby town but to an entirely different country altogether. Of course, it was set up to make look like it was an accident that something went wrong with teleportation magic. Lutz would not be aware that it was intentional at all as unable to use such magic himself on top of not realizing the true nature of mages of the Valia either. Regardless of this, he was going to attempt to return home however that would eventually prove harder than he would think since would not know the way. They were just hoping that even if he did attempt to return he just die or something the way thus would not get their own hands dirty doing it themselves.