Nah b/c Phil is the highest ranking dude on the streets now.
Johnny Sack did all that warring to be boss on the street for like 8 months
When indictments take out the upper echelons/the admins (boss, underboss, consigliere, high ranking capos), the family doesn't fold, they just bump new people up to the positions, the boss with implement a "street boss"/Acting Boss on the street (remember back to S1, tony's homie Jackie Sr. was Acting Boss when the other boss was in jail).
A mob family isn't just like some drug clique, where once the leaders are taken out the whole thing crumbles, the family is bigger than any one member or group of members, especially an NY 5 Familiy. The mob families IRL, even the jersey family have been around since 1890s or so and still exist. Only the real small families (tampa, FL) have been defunct...all the major ones (NY 5, jersey, philly, chicago, detroit, buffalo) are still functioning to this day.
At their peak, the Gambino family had something like 250 members, 21 capos with 21 different crews...and that's just one of the NY 5
they want someone close to Tony, Bobby
and then the 
