The primary factor I think, that's going to preclude a full return of a Federal Government to the District, more then anything else, will be inertia. The Great American War will see the Federal Government rapidly expand both in it's powers, and it's bureaucracy. After the chaos of the evacuation of D.C subsides and the Hughes administration settles down in a nice Northeastern/Midwestern city, whichever provisional capital they pick is going to inundated with Federal Departments, relocated cabinet officials, and a large and rapidly expanding Federal workforce as the country shifts to a war footing.
After the War ends, the cost of moving all the Departments and their workers back to a war torn D.C will probably exceed whatever will exists to one up those damn Southroners. Not to mention the electoral implications of moving all those (presumably Liberal voting) Civil Servants who now reside in a nice (Midwestern/Northeastern) swing state...
And even if they do decide to shift some functions back to D.C, I doubt it's going to be anything close to a full return, for instance, I don't think the War Department is say, going to place the alt* Pentagon anywhere south of Maryland anytime soon.
Though speaking of the War Department, this is what the National Mall used to look like after they finished building a bunch of office buildings for the War Department. I'm pretty sure those are Walkways over the Reflecting Pool. So, the new construction the provisional capital can expect.
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