You may consider this a spinoff of the debate over whether Washington should get Senators, etc.
Washington, DC made pretty good sense as the location for the capital in 1800; arguably it makes much less sense today. It’s located far on the East coast. However, the mean center of population keeps moving south-westward. Sure, the Eastern half of the country has quite a lot of people, but we keep growing on the west coast and points in-between. Even apart from that, growth in the .
To that end, why not consider moving the capital and getting past the political problems of Washington? We could create a new capital located around the borders of Missouri, Arkansas, Oklahoma, and Kansas, with appropriate borders and rules so nobody ends up feeling like they’re left without representation. Some major departments (especially the Pentagon) could be left so as not to instantly gut the Washington economy.
Finally, we could build and plan the new city of, eh, call it “Columbia” for now. It’s a relatively open part of the country so the cost would be relatively low in terms of land, the city would have a large build-able area, there is water available, and people could potentially commute from at least four states giving them a reasonable choice of where they want to live. It would be also easier for much of the country to get nonstop flights to the new capital, while potentially helping build national infrastructure in what is now an out-of-the-way location - but which could become a bigger artery of commerce and growth.
Brazil did exactly this in 1960, establishing a new city (and new capital) called Brasilia, which is more centrally located than the old capital, Rio de Janeiro.
I don’t know enough about Brasilia to know how well the move was implemented, unfortunately.
That area (at least the part in Oklahoma) is Tribal Land currently occupied by a Native American casino. You probably don’t want to recreate the Trail of Tears.
What are the political problems that are so bad that this enormous change is justified?
I mean, I’ve read science-fiction stories that describe a new capital built after the destruction of Washington, DC. But since that hasn’t happened, why would we want to do it now?
Actually, due to climate change, much of DC might be under water in fifty or a hundred years. But Republicans assure us that climate change isn’t real, so that’s not a good reason.
I cannot see any real reason to move the capitol, or the capital. That said, we really ought to move major Federal facilities to other areas to spread the wealth and increase security from a cataclysm.
Why does the IRS have such a huge presence in DC? The Coast Guard? Agriculture? In this age of communication a lot of back office functions can be moved. Maybe they should be.
Largely because of interactions with Congress, and with other Federal agencies, I would suspect.
Could they be more decentralized now? Sure, but that’d be expensive, and you may well lose key agency employees who don’t want to relocate. A couple of years ago, the Trump administration announced plans to move a number of USDA researchers from DC to Kansas City, which may have actually been an effort to purge the agency of people that the administration did not like.
(Edit: it was actually only last year, not “a couple of years ago,” as I had written. I blame the fact that 2020 has been 7 years long. )
And IIRC the Potomac as far up as DC is still tidally influenced so some serious infrastructure work will be required…
Back to the OP – With the communications and transportation resources of our time, there is no real need for the capital to be located at the “center of mass”. Now, about this particular aspect:
That sounds like the idea is to start anew a Seat of Government and this time avoid it organically developing a nontrivial resident citizenry that would argue “disenfranchisement”? Locate it where hardly anyone already lives, then plan it as a minimal Government Post, containing only government buildings and garrisons, and no actual “permanent resident” therein but let the whole workforce commute from the adjoining municipalities, and only let live within limits those who are known to be there only for 2/4/6-year increments of tour of duty, who’d keep their "residence’ in the prior state?
And some entities are spread around already. Sure, mostly they’re spread around Northern Virginia, the East West Virginia Panhandle, and Maryland (e.g. Social Security and Medicaid/Medicare are in Baltimore) (CDC is notable for being all the way out in Atlanta) but the office of any cabinet-rank head usually remains inside- or immediately-outside-the-Beltway so they can get summoned to the WH or the Hill at a moment’s notice.
I don’t really see this as a good idea. The OP can speculate that the cots of building a new capital in the middle of the country would be low. But that cost is obviously higher than continuing to use the capital whose construction we’ve already paid for.
What would happen to all of the historic landmarks that exist in Washington? Would we operate them as historical monuments? Another unnecessary expense.
We would also have the cost of relocating all of the employees, records, and equipment of the federal government to a new location.
And within a fairly short amount of time, all of the problems people have with the existence of Washington today would arise in the new capital.