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.