IMHO, I smell a classic double-cross.Barzini uses Tessio to lure Mike to his death,then also whacks Sal for good measure.Barzini is an old school, cunning, ruthless Don who would never trust a man who betrayed his boss.

Barzini's whole motivation is to destroy the Corleone Family,first by chiseling into their various rackets in New York,then by attempting a Vegas takeover through Moe Green,not to mention basically taking the lion's share of the Narcotics trade.

Barzini has no need for Tessio at all. Hagen would have no connection to the Family anymore except maybe making sure that Connie is taken care of. He can easily transition to legitimate business and retire safe and rich.

Barzini, by this time has had about 5 years in the Drug business,so I'm sure he has built up enough political contacts and protection on his own,so no need to involve Hagen.

Neri and Rocco would not be a threat. Since there is no Corleone Family any more,what would be their motivation ? Revenge ? Barzini' would see it coming a mile away and they wouldn't get near him.Same with Clemenza. He would be out of a job unless he could put together a little side racket. Bottom line is there would be no sense fighting to regain the Family business since the Family business would have died with Michael. Just my two cents worth.