What keeps the Deep State alive is vulnerable to the stroke of the President's pen. Without JFK's Executive Order legalizing them, there would be no unions for Federal employees, and rank-and-file bureaucrats could be dismissed at will, just like the "political" appointees.
President Trump could begin the destruction of the Swamp with a signature--no more secret, unaccountable hands working for the American taxpayers' domestic and foreign enemies.
Yes, that would be a good start. Civil service protections might be appropriate for line-level law enforcement officers and postal workers, but they make a lot less sense as you get higher in the org charts.