We have already tried privatization, and it turns out just to be another form of crony capitalism. What you need is someone who will appoint cabinet officers who will decide what needs to be done for their departments to serve the interests of the American people and then make the people in their departments do those things and take them out if they do something else instead.
It is hard to fire a federal employee, but you can side-line them if they are in the way.
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.