The Federal Beaurocracy has awesome power, that can be abused. We all see that. Its tempting to give POTUS authority to replace people who wont implement his agenda with more like-minded individuals.
This is an even bigger danger IMO.
I might trust Trump with this power, but probably not the next POTUS. How about being able to hand-pick every member of the FBI, CIA, IRS? Who would you trust with that ability?
You bring up good points. But as long as elections occur, those who abuse such power are prone to be replaced by an administration who can also purge the executive branch. An abuse of power carries the consequences of prosecution be the next administration, and so on and so on.
So in your world, the FBI is not in the executive branch? The CIA should not answer to the president, but should lurch forward in the direction they feel is best without a pesky president bothering them? No thanks