What you are proposing is something Congress would have to do. The president can propose such changes, but Congress would have to eliminate any departments deemed unnecessary, since they were established by law. How likely do you think that is?
And in the absence of any such action by Congress, what should the president do? Should they whine about their inability to make any changes? Should they attempt to ignore the law, a la Obama, and try to close the departments anyway? Or should they use what powers are legally and constitutionally available to them to reduce the size and scope of government as much as they can while continuing to try to get bigger changes through the Congress?
OK so let's take Fiorina's plan. If 10% of your judges retire then what does that do to trials if you are handling the same caseload with fewer judges? Or fewer prosecutors? If 20% of the air traffic controllers retire then what does that do to the air traffic system in this country? If 15% of Fiorina's Secret Service detail retire then will she limp along with less protection? If 15% of the CIA or the NSA retire then what does that do to our security? If a fifth of your Border Agents retire then how do you seal the border? If 20% of the Department of Defense civilian workforce retire then what does that do to our military preparedness?
It's an asinine plan. It's the plan of the fifteen second sound-bite and not a rational idea for shrinking government. It's the kind of plan one would expect from Carly Fiorina.