Man-pain? I didn't know Snyder directed this show too!I don't think that was the case, either. Right before he assaulted the marshals that got him thrown in jail, he was about to buy a plane ticket to the most isolated place he could find. It isn't so much punishment as it is isolation. He has somehow conflated his physical presence with the pain, violence and death that his bad choices have brought into being. He puts himself in jail so he won't be around to hurt his friends anymore. A concept that is undermined by the ease with which he escapes later, but don't tell the writers that or they might have to think a little bit next time.
And then the ultimate revelation Dick has isn't nearly as meaningful as the writers want to portray it either. He realizes Jericho is still alive, and is thus absolved of his guilt for killing him. But Dick never really has to accept that Deathstroke and Jericho both made choices. It really shouldn't be about Dick's man-pain, it should be about Jericho's sacrifice to save him. But to the writers, and thus Dick, Jericho's agency is meaningless and his choices aren't worth giving credit to. Rather than Dick accept that Jericho chose him as a brother and gave his life to try and save him, it becomes about Dick's grief that he killed Jericho and his joy that he doesn't need to carry that weight anymore.
They could have used Dick's acceptance of Jericho's choice to strengthen Dick's resolve, and his later realization that Jericho is actually still alive to drive him to action to repay the deed. Instead, Jericho is used as a prop for Dick's pain and insecurity with himself. The ultimate irony is that, as presented, Deathstroke gave more concern to his children's agency and choices than Dick ever did. Even if his response is disappointment and anger, at least he acknowledged that they made choices on their own.
I didn't totally get why Dick blamed himself either. Slade killed Jericho.