I don't know how large Sonny's regime was. But he created one/took one over in the aftermath of his father's shooting during the war against the independents. At that time per novel he made a reputation as "the most cunning and relentless executioner the underworld had yet known".

So presumably at that time both he and his direct reports were getting their hands dirty. Perhaps since at time of movie Sonny is underboss with presumably greater responsibilities his regime's primary job during war to just to guard Sonny and not be involved in front line attacks? If Sonny's regime was less than 20 guys, as opposed to the hundreds that Tessio or Clemenza could command that might explain it.