Cobra wasn't pushed out, he left because he wanted to smoke and drink but his dad said "not while you live under my roof", and that motivated Cobra to go to Job Corp and later to work at Wendy's. In the beginning his ODD was a net positive, he ended up flying solo and learning responsabilities of adult life, towards the end he needed some kind of intervention.
Clint was as close as Josh allowed him to be, i think. The main problem is that Cobra just wouldn't do what Clint told him to do, so i guess Clint didn't even try to tell him what to do anymore, which is probably a reason why there should have been some intervention to give Clint some level of authority over Cobra. I don't know how that works legally, but Cobra was in poor health and lacked the self-preservation instinct, so Clint should have been allowed to swoop in and put Cobra in a home.
I think he didn't do it because he knew Cobra would hate him forever and because he felt bad for Cobra, he kinda put his own personal feelings for his son over his son's well-being in a way, which is selfish but understandable if you analyze the situation.
I don't wanna blame Clint or talk shit about him because if his inaction was what lead Cobra to drink himself to death, he's gonna carry that weight till the end of his days and that's punishment enough for a father.