Very dissapointing.
MC got chained, sued as blackmail material, pierced by a sword twice with his life threatened...and he wants to save who did all of this.
Suicidal empathy at its finest, a born puppet...
I'm guessing that the dragon wants to be put under domination because she can leave the dungeon that way, got incredibly bored of being there but as a master can't leave the place even if she tries, but under domination she loses that status or the system allows exiting, but at the same time she doesn't want just anyone as her master.
This is all just a guess but as sshe wanted to meet who had that skill and didn't kill MC on the spot is clear she wants to be put under it.