Tony wasn't shyt, through and through. They made it a point to show that even his therapist realized that he was USING their therapy sessions to become a sharper sociopath.
The genius in the show is that Tony manipulated his therapist AND us viewers into liking Tony and thinking there was something good in him, that his deep reflective sessions was a deconstruction of a good guy that is bad by circumstance. But his therapist recognized that Tony wasn't a mob boss with a heart of gold, like she and us viewers wanted him to be. Tony was just so charismatic and intelligent, such a good talker, that he managed to hide his nature even while exploring it. And a sociopath that intelligent can't actually use therapy to better himself as a person, he just humors it to better justify his actions and thoughts as a criminal, cheater, murderer, racist, apathetic father and spouse, etc.
Or as said on the show. "Talk therapy, while not only being useless with sociopaths, actually serves to validate them. They sharpen their skills as as con men on their therapist. Crocodile tears, what have you. They showed data. The one year re-conviction rates were higher for offenders in therapy than for those receiving no treatment at all."
The decency we think we see in him is just a facade. An illusion that we force ourselves to fall victim to every time we see him dealing with a family crises and extrapolate his experience into something we could relate to if "we were in his shoes." And it's that quality that an intelligent gangster like him uses to gain trust in people that absolutely should never trust him, including his business partners, wife, friends, and children.
That's the genius of his character. He conned us all because we loved him, just like his family, friends, and doctor