The distinguished historian, Michael Beschloss, sheds some light on that:
In his book on LBJ's first year in office, "Taking Charge," which is based on recently revealed Oval Office tapes that LBJ made, he has transcripts of several conversations between Hoover and LBJ, and RFK and LBJ. As soon as LBJ returned form Dallas, Hoover was in the Oval Office, ingratiating himself with the new President and becoming his exclusive source of info on the assassination. In a later conversation, RFK complains to LBJ that he has no ability to influence Hoover--if he ever did (Hoover had the goods on both Kennedy brothers; see my post on Hoover above).
But to the point of a new Attorney General: LBJ treated Bobby with unfailing courtesy, Bobby treated LBJ with undeviating contempt. The reason was political physics: LBJ was paranoid about Bobby using sentiment for the slain JFK to mount a run for either President or Vice President in '64. Bobby knew that, with his brother gone, all of his White House influence was gone. In the end, RFK solved the problem for LBJ by resigning as Attorney General well before the '64 Convention and running for US Senator from NY instead.

The Federal Government's ability to prosecute Mob figures was limited before passage of the RICO Act: they had to find "interstate" components to Mob crimes, which usually fell under the vague rubric of "racketeering." They could subpoena Mob types, but if the Mob types pled the Fifth (attention: Michael Corleone!), they were practically immune from prosecution. The only other prosecution venue was tax evasion. RICO gave them the power to move against the Mob, and success propelled further prosecutions.