Obviously staying around won't work for Hazou, but he doesn't seem like a quitter, and he still believes that he can be useful to the team.
Just not by being with the team.
He and Kagome are unfit for society. Thus, they leave society.
[] Action Plan: The Watchtower
does exactly this. Suicide doesn't help at all, but he would (correctly) assess that being with the team is hurting them more than helping. His usefulness has been primarily in his seal ideas, and he doesn't need constant contact with the team to get those. Maximum usefulness to the team while minimizing the harm that he can do.