Back then there were only 13 states and each of them were very jealous of state versus federal power. Each state back then would have been concerned that the first state with the national seat might have become the metropole (ruling state) of an empire with the other states as the peripheries(subject states). The USA of 1787 was a lot closer to a federation of smaller nations (states) than anything else.
As far as the Legions in Rome? The Senate kept the legions out of Rome proper to prevent a consul (aka General) from conquering Rome and becoming a tyrant. It was a check against military power. DC was a check against the states power for the federal government.
Now DC happens to be metropole of the Washington DC Empire and everywhere else is a periphery state (the states). It's exactly what the founders feared.
Thanks. Appreciate your explanations.