After Tony's murder,there is no Soprano Family to speak of. Assuming that it was the Lupertazzi Family that killed him,(since no one else had a motive to do so, or the power to pull it off) there is no incentive to give Paulie anything but a bullet in his head.
If Paulie helped to set Tony up,he's branded as a traitor by the Luppertzzi's and in line to be the next to go(just like Caponigro got double-crossed when he hit Bruno).
If he didn't set Tony up,then I doubt that he would be made even a token Boss.
Paulie is really the only one left as far as being a major player in the Soprano business. The smart move is to swoop in,take over the whole operation,and put Paulie to sleep.

IMHO,there is no business sense in giving Paulie any of the Soprano business,or bringing him into the Luppertazzi Family.

He would be a permanent pain in the ass,and would never be trusted to not make some kind of move against Butchie,(or whoever)
Bottom line,with Tony dead,and Sil beyond recovery,there is no need for the Lupertazzi's to give anything to anybody outside of the Family.
Take out Paulie,and they get the whole enchilada.