The FBI needs to do a better job of communicating to the public the existing oversight mechanisms it has, as well as reporting in aggregate types of issues it has prevented through the use of the authority. Additionally, more frequent (quarterly) testimonies to Congress (closed and open sessions) would be extremely beneficial.
If the FBI actually operated in the open and stopped keeping secrets, the mystery would be removed and they would no longer have any power. Once the mystique is broken, the mundane reality of the FBIs daily ineffectiveness would be revealed. Power requires secrets. What you are suggesting would destroy the FBI.