Your plan sounds like a great idea and sounds like something Trump would insist on doing. I know it's currently hard to fire deadwood, but can't that even be changed. What about public sector unions? I would hope everything is on the table to at least take a look at.
Let's face, who besides Trump would even investigate various departments, entrenched bureaucracies, do some downsizing and cut the deadwood. We need to run the federal government as a business not a bottomless money pit. It's Our Tax Money and if you define taxes as 'theft of income' then it makes sense for all of us to be interested in a complete top to bottom overhaul of the Federal Government. It will never be efficient if it's 'do whatever you want' in every department.
A Fed employee once told me your promotion up the system depended on how many new people you hired and how many departments you were able to create. You were labeled a doer then. Now that's just the opposite of the way a private business would look at it.
While there is a lot of dead wood, the top guys in each office are often pretty good. But for each assistant secretary there are a couple of Schedule C employees (unconfirmed non-career positions controlled by the white house) who serve as white house handlers to keep tabs on what is going on - the American version of Political Commissars. In the Ozero administration no one can do anything useful. Bush II was actually not a whole lot better. Really! A good bit of the expansion of DC beltway banditry was funded through DHS which was created by .... Bush/Cheney.