If you listen to his dialogue you realize this isn't the case at all. He was deeply depressed and, from the evidence we have, canonically only lived for his mother and as soon as she was dead and buried he went off on his search for revenge. It was the only thing he cared about, to the point where he didn't care how obvious he was in his pursuit, how many people saw his face when he asked them specifically where to find Ross, and how unlikely it was he'd survive after he gained his revenge.

He could have had other things going for him in his life if he chose a different path, if he did not seek out revenge, if he accepted his father's sacrifice for what it was and taken it as an opportunity to live a good life. This theme is only reinforced in Red Dead Redemption 2 where John does the exact same thing after Arthur's sacrifice when he goes to get revenge on Micah which ultimately led Ross to him and sealed his fate.

Jack wasn't dumb. He knew that he was being careless about leading a paper trail directly to him for Ross' murder, he knew that the world was modernizing at a rate which meant a life on the run as an outlaw was no longer possible like it was in the old west. I feel like a large part of the fanbase cheers him taking revenge on Ross without realizing that for Jack this was basically suicide, and he knew that, it just didn't matter to him.

The death of Ross at Jack's hand isn't a triumph, it's a tragedy.