According to FBI and informant reports Battaglia didnt want the top spot and was forced to take it. Plus at the time Battaglia wasnt the major money maker within the organization and also wasnt the most likeable person among his associates like Alex and Buccieri. The things was Battaglia was very close to Ricca and was also going on many fishing trips with Accardo

Ricca and Accardo were like "trainers" and they were always grooming other members for the boss position. So i think that this pretty much made their voices big on many major decisions. Even back than the FBI knew that these guys were in charge but the thing was that they were not involved in day to day operations so it was very hard and almost impossibile for the government to catch them in any wrong doings. Thats why the government always tried to deport Ricca from the country because they knew that he was the one pulling the strings from the shadows.