I know about that idea of deferring decision from un-elected to elected authorities. But, the problem is nobody elects NSA hierarchies. Or FBI, CIA, etc. And they have such amount of power that THEY decide over elected officials, and not the other way around. No president can take a decision against what the powers inside the NSA want. The officials nominated by the president to head those agencies are either guys imposed to them from within that agency, or a nominal authority with no real saying in the power structure inside.
The more you think about it, the more you realize is a catch-22.
When you elect a president, you're also electing the leaders of the DoJ, DoD and NSA.
This is such a fundamental concept in our system of government that the Constitution spells out a check and balance system for principal officers of the USG.
Note that all of those positions are also approved by the legislative branch through Senate confirmations. The only unique position is the Director of the FBI which holds a 10 year appointment.