The reason Kenji said this was partly because he genuinely believed that establishing an independent department would be better for handling this, and partly because...
The emperor didn't seem particularly eager to hand over educational authority to him.
Understandable, considering that Kenji's influence was already quite extensive. Military affairs, politics, food security, and more were all under his purview, and recently he had even been involved in imperial family matters (although temporarily, just to eliminate Yunis). Even now, the actual Director of family Affairs was still very angry with him.
If she were to let him freely control education as well, he would have to seriously question whether she as the emperor was thinking clearly.
Evidently, Pluvia understood this point, so she very decisively chose to entrust educational authority to others. From Kenji's perspective, this wasn't a bad thing either.
