Even Carmella was frightened of the prospect of Paulie looking after the Family if something were to happen to Tony.

The family is in ruins, the top guys are all dead, Ralphie, Chris, Bobby, Silvio, Vito or have collaborated with the Feds, Eugene, Carlo, and Ray Curto.

Tony was already broke by the end of the series, and without any guys out on the street (maybe the Bareses), then he won't have enough cash to fight a lengthy trial.

That being said, we have Paulie as one of the higher ranking members and he finally would get what he wanted, respect with NY and "to bring good relations between the families". Unless Uncle Jun has miraculous recovery, Paulie is the Boss.