Dude, its death games. Kinko fumbled and let Aoi die, Beniya wasted time for selfish reasons. And if the first girl had survived to make 6 for the first game, there would have been even less time to get the keys to everyone.
And if more survived, more limbs would have to be chopped off (like yeah they can be reattached but its still traumatic). And Kiniko being left behind meant she would of died anyway.
While I'm line 99% sure this is a fetish manga, its not completely pointless to argue morality, logic, and human fallibility due to predisposition and societal value influences.
You can say Yuuki is horrible but she literally has no choice. When you sign onto these games (for the most part), you submit yourself to the dictated rules of the rich and powerful (much like real life). How many people are actually going to be selfless and say they will sacrifice themselves? How many will turn around in a group and say the person with the least to live for, like Yuuki, should be the one to die and how does that make it right?
You can die morally right but nothing will change. So its back to the most base of instincts living beings have, survive any way possible.
