Supposed to where? Is it in the federalist papers? Are any of the founders known to have elucidated such a barrier? Is there a law that has been passed declaring such. Or is this just your opinion?
Law enforcement falls under the executive branch, which has only one elected official. Two of you count the VP, but no one does. It is specifically the president's job to oversee these bureaucracies.
What you are advocating for is an uncontrolled regulatory state, which is sorta what we have right now and it sucks. For the people, by the people.
If the president isn't directly engaged in the management of the FBI and all of it's functions, then we the people have no recourse to change the FBI when it, let's say hypothetically, launches an investigation knowingly based off opposition campaign research, eventually lying to the FISA court in order to obtain warrants to surveil Americans who are participants in the nation's most important political process.
Your perspective on this particular issue is perfectly demonstrative of the failing of liberal thought. The system should work this way. Best practices. I don't want. It shouldn't be. Ideals.
An idealist would create an independent FBI and think that it will act in accordance with everybody's fair-minded values, even though there is no agreement on what is fair-minded. Conversely, our entire system was designed explicitly acknowledging that idealist independent systems will always devolve to tyranny, and instead used checks and balances amongst the competing branches of government in order to rein in the inevitable corruption and political posturing that would follow.
An independent FBI is precisely what Americans should fear, and the history of the organization is so laughably demonstrative of this that I'm surprised you, usually historically aware, would think otherwise.