We used to have that back in Andy Jackson's day. The incoming president could clean house and not be stopped by civil service regulations.
What's needed is
1) Eliminate civil service protections. Let the president and his cabinet secretaries fire as they please, and
2) Limit Senate approval to just the cabinet secretaries, and maybe the first-level under-secretaries. Let the secretary hire whom he pleases.
Your solution is a lot better than what we have... but a compromise might be to rotate the people in DC to other Federal jobs in flyover when a new party takes over the capital...