Back in Andrew Jackson's time, there was no "civil service" job protection. The incoming President had the power to fire all of them, and put in his own people.
Perhaps we should reduce the level at which government employees get civil service job protections.
That's my point - Congress is, at least, elected by the people. No one elects the millions of government employees, and their lobbyists, political ideologues and cronies within government. As you say - limit their tenures first.
I put in an earlier post - put every government department and agency on a 20 year automatic expiry. Congress can decide then whether to renew them or not.