I completely sympathize with that dad. Instilling any kind of discipline into that girl is clearly very very difficult. Her dad probably takes whatever shallow victories he can in trying to get her to behave like a member of civilized society. And now suddenly she can easily acquire more money than she knows what to do with. How can he be a parent to her when she can just say "fuck off" and live on her own? What kind of lesson is she learning when she has enough money to avoid anything she finds unpleasant? Who will be there to watch out for her and stop her from doing something with real consequences—like prison, or permanent injury?
As amusing as Hibiki is to read about, she would be incredibly stressful to deal with as a parent. Her dad isn't the bad guy here. He's trying to refuse the money because he's worried about the long-term well-being of his daughter.
Accepting the money and using it all to pay off a debt she owes is fine as well. If all that money she earned disappears because of some stupid stunt she pulled, then maybe she'll learn to be a little more careful. I doubt that will actually work, but it makes sense at least.