First of all, Accardo was never THE BOSS, he always reveled in his role as consigliere. He held the underboss position for a short period of time (on several occasions), but he was not a fan of the responsibility.

If we're talking longevity, Paul Ricca was the most successful of all-time. If we're talking numbers, Joey Aiuppa, hands down was the richest. And if we're talking fame & glory, Moe Giancana takes the cake always. Accardo was interesting because he sort of balanced back & forth between those 3. He never really kicked his alcohol & gambling addictions, so considering him for boss was always naturally out of the question, but he never went for power plays anyways. Instead, he managed to stay relevant throughout 3 Outfit dynasties (Ricca, Giancana, Aiuppa/Cerone) & always make himself & his crew useful. He had no qualms about being the fall guy & always remained loyal. He toyed around with getting clipped/whacked when he purchased his River Forest mansion in 1953 & began holding massive, lavish parties, a HUGE no no within the Outfit. Giancana abruptly put a stop to that & the mansion was sold in 1961, with Accardo moving to a more modest, unassuming location.

So getting back to the point at hand, Joe Batters was never the boss, but he never really wanted it that bad anyways. I actually find him to be one of the least interesting figures throughout Outfit history.