If this speculation could become successful, perhaps, Link was on the verge of creating a new wizard sect.
In the Wizard World, there were more than just the five major schools of Elemental Wizards, Body Refining Wizards, True Spirit Wizards, Intelligence Mechanism Wizards, and Beast Controlling Wizards.
These five major schools all had sages at their pinnacles, defining their ideological paths, nothing more.
There were also some branches based on the five major schools, or a collateral branch unrelated to the five major schools.
These medium and small sized schools stand out on their own, each with its peculiarities, lacking only a strong figure standing at the top of the school.
In Link's speculation, the school that might be initiated would not be pursued by him personally or the members of his direct line who were "free to do whatever they wish".
However, it could be used to cultivate non-direct line subordinates.