It doesn't make sense. It's set up that way for historical reasons, and because the folk in charge have always really prioritised 1) over 2), and hence have had no motivation to suggest a better alternative.
While a separate organisation might be best, even a division within NSA etc. explicitly tasked with protection rather than intelligence gathering would be preferable to the status quo, so long as its head could be publically known. In the end it comes down to there being no individual with that responsibility. You need someone who is visible in that role, whose mission is purely to protect, overseeing a staff whose mission is purely to protect.
While a separate organisation might be best, even a division within NSA etc. explicitly tasked with protection rather than intelligence gathering would be preferable to the status quo, so long as its head could be publically known. In the end it comes down to there being no individual with that responsibility. You need someone who is visible in that role, whose mission is purely to protect, overseeing a staff whose mission is purely to protect.
What am I missing?