The Founding Fathers organized things they way they did for good reasons, and with a knowledge of human nature.
"Well, suffice to say that in the long run, that may not be such a good idea."
The FBI tried unsuccessfully for months from obtaining what they wanted from Jefferson voluntarily. And now we have to set up protocols for the FBI to execute a search warrant on a member of congress. That's just plain crazy and they, Congress, are putting themselves above the law of the everyday average Joe citizen.
The Founding Father's put exceptions into the Speech and Debate Clause.
They shall in all Cases, except Treason, Felony and Breach of the Peace, be privileged from Arrest during their Attendance at the Session of their respective Houses, and in going to and returning from the same; and for any Speech or Debate in either House, they shall not be questioned in any other Place.
Treason might apply as well if there is hostile foreign government involvement.