Not every Royal has the power, only a few have the "wisdom eye" which allows them to see the rarity level of things. So those few are probably not allowed to marry into noble houses, but have to have spouses marry into the royal family. (Maybe the king had an eye on MC because he was looking for a reliable son-in-law who could marry into the royal family).
The priest probably reported this new unknown job to his superior, but until this reaches the king will take a wile, especially because nobody outside the royal family ever heard of "rarity" and that jobs, related to it, are important.
The father kicked his son out on the very same day, long before the king had any chance to intervene. And the father said he would only accept sword saints, so he would have kicked out MC anyway, the moment he got any other job.
But we all know the father will regret his decision later on.
That does make sense
So the fact that things have a rarity is a secret only royalty knows (let's put aside the fact that it makes no sense for nobility not to know since I expect royalty to marry nobles and once the bloodlines mix the ability to see rarity shouldn't be exclusive to royalty), which makes a job like "rarity changer" a mystery to everyone else. This is fine BUT I would expect people to try to research it a little bit before dismissing it entirely. Did nobody report the "birth" of a new job to the king? It always makes no sense to me （￣へ￣）