There is a theory that since TADC is based on I Have No Mouth and I Must Scream, each of the characters is the show based on one of the characters in the story. Along those lines, Jax is based on Ted, the narrator of the short story. Ted and Jax are both narcissistic, cynical assholes who actively make their companions lives worse. They both pretend to be unaffected by their situations, but both are liars. Both of them might have good traits, but are buried under the suffering they have endured and the situations they are in. Both of them turn into some horrific looking monster at the end, forced to live that way forever.
The difference is that Ted redeems himself by sacrificing himself for the other victims of AM. Deep down, Ted was a good person who altruistically sacrificed himself for the others. Even though Ted says and does vile things in the book, he still redeems himself through his actions in the end. Jax, on the other hand, especially because of the ending, is now just a dickhead that takes his sexual frustrations out on others. He is a perpetual buzzkill and burden, and then he just turns retarded off screen and we are supposed to love him for it and feel sad when he does.
Following the show, it really seemed like the story was trying to redeem Jax, but that closeted crossdresser deserves none of the pandering or coddling at the end. We could have learned more about ANY of the other characters, but we get stuck with the edgy self-insert.
Either that or Coop hates that people like the character he was trying to make unlikable so he just throws him under the bus at the end.