"The vice president in this case is like the queen of England. You can't even buy airline tickets without talking to someone like me. Therefore, let me speak to the White House because, I can assure you, I'm the one person who can make this all work out."
--National Security Advisor Jack Doherty (Air Force One)
Taken from this missive, the below timeline indicates when cabinet-level departments were instituted in the federal government. By my count there are 16 cabinet level departments with nearly half of those established since 1950.
I can see merit in the first four: defense, treasury, state, justice. Why? Because they can be readily tied to executive powers granted in the Constitution.
The farther away from the founding other departments were established, the less constitutional grounding there seems to be.