http://www.cnn.com/2016/09/06/opinions/government-departments-should-be-spread-out-price/?iid=ob_homepage_deskrecommended_pool
"In one bold move, it would bring the federal government closer to the people, reduce the threat a major act of terrorism would pose to our nation's capital, and create new jobs and new infrastructure throughout the country. But, perhaps most importantly, it would renew faith that our government exists not to serve the wealthy or the connected, but all the people.
No, not the White House nor the Congress, but the rest of the federal government, namely the Cabinet departments and large agencies that have grown up around the Beltway, should move and disperse. There is really no compelling reason that federal agencies and departments remain in Washington, D.C., and many good reasons why they should be relocated across the United States over time."
The key is over time.
This is actually a great idea, and I have been thinking along the same lines. Unlike his recommendation I would consider areas of economic depression for the location that also fits the role. Des Moines is doing well, and does not need the Dept of Agriculture, but perhaps Memphis? Dept of Transportation to Detroit? Department of Energy to Houston? What I don't like is wasting existing infrastructure.