Riku killed her because it was what she wanted. She commanded him to do it, and he has been loyal to her for centuries, so he obeyed. I thought it was a pretty good choice, and it also gave her a chance to say her last words to her brother, since Kirinmaru still hears what Riku hears.

Although she didn't kill anyone, she robbed the main cast of being a family for over a decade. She can't return those years to them, and even if she helped taking down Kirinmaru, would that really make up for what she did? I don't think it would, really.

The only alternative I could see here would have been exile. Leaving Japan forever and never interacting with the Great Dog's family again. But I think a voluntary death was fitting too.