That doesn't make much sense to me. The firms that rent office space on K Street don't have power because of the location of their office... it's the other way around: K Street real estate is rented out by those firms because of the street's proximity to power.
Move the power center and the firms currently renting office space on K Street, DC, USA will instead rent out space on Blah Street, Middlepoint, USA.
More-over, I don't know if moving the capitol of the country to the median point as defined in this article makes any sense either. It's one of those "literally everyone loses" propositions because "median" isn't "modal". If anything, it could make sense for the capital to be located at the midpoint by travel time.
But it's all wildly impractical if you stop and think about. The amount of infrastructure alone would require decades of work. And states would have to surrender sovereignty over a big chunk of their (settled!) land. Etc.