Because he wasn't a very good leader. John has his qualities, good and bad but a great leader wasn't one of those.. that much is obvious. Even as a capo, his friendship with Dellacroce was probably the ticket, because his crew wasn't good for much other than dealing H and the occasional hit, which they weren't even that good at.
Plus why would Paul use the Bergin crew for hits anyway, when he had the DeMeo crew at his disposal?
I could see why Paul didn't like him that much... if I were him, I'd have tried to nip it in the bud and shelf him a long time ago, putting somebody else in charge of his crew.

@DuesPaid: I agree... for the life of me, I can't understand how most of these guys ALWAYS let greed get in the way of doing the right thing and giving some $$ to the family of a solid, stand-up guy who's doing time and probably getting out in a while.
Even the Camorra does this.. they should have taken a page out of their book.