Found these good points online so thought I'd share.

Hear me out. I realise that the actor was arrested and canned from the show, and that's why we never saw any more of Albert after season 5. But he is actually the best contender for boss of the family after Tony's death. This applies whether Tony was taken out by New York, or someone else, and whether or not Paulie or Patsy were involved.

1. The Barese crew is the largest by number. This means anyone in the top job needs the approval of their capo.
Albert and Paulie don't get along ("that fucking Parakeet!"), so I doubt Albert will accept Paulie as boss.

2. Albert is a top earner. 'Do you know what Albert kicked up last week?, and the crew has relatively legitimate business interests with the garbage routes ('the trucks.').

3. Albert is a savvy operator. 'It died on the vine' — He is extremely careful not to compromise himself in a family wired for sound. Same with refusing to follow Ritchie's attempted coup

4. Albert is not caught up in the recent war and the bad blood that has arisen. This was largely a beef between upper management, Soprano crew, and New York.
Paulie and Patsy are compromised by their proximity to Tony and won't be seen as trustworthy.

5. There is no other contender. Paulie is unreliable, earns little, and has no crew (other than Little Paulle). New York simply won't trust him.