What made that particular governor qualified, though? She's probably just someone the queen has personally trained, with zero personal strength. She's someone only as long as people recognise her official authority. If Kakyu had a different sort of personality, and he actually cared (had the ambition the queen saw missing), he would keep ignoring the governor and doing things his way. The more he involves her, the more power he gives her and removes from himself. But alas, even after 2000 years in Hell, Kakyu still has a solid Japanese salaryman mentality. When the queen told him the governor is the senpai, Kakyu's fate was sealed.
I'm really thinking he should let it be. He's not suited for an actual noble life. So, being a landless noble is better for him. He's as powerful if not more powerful than the gods of that world, so why exactly does he need to slowly gain the royal house's trust to figure out what happened to Erza? He could probably just invade people's minds in their sleep and gain the information that way. He's an overpowered demon, after all. Invading sleep and possession are their natural talents.