Edit: Capital vs Capitol mistake
Earth is the capital of the Federation. Just in regular space traffic alone Earth should be swarmed.
The amount of small Starfleet ships analogous to harbor patrol and coast guard should be enormous. And they're very likely lightly armed if nothing else.
And I think comparing Earth the capital to a bureaucratic facility on a major landmass is the wrong tack. It's basically a space island in a little archipelago. Its surrounded by space-water. With all sorts of facilities all over the system, unless the teleporters can teleport that far, that means ships and boats just to get around.
The academy for Starfleet is on Earth, the shipyards are in system, the design institute, the Capitol Federal government buildings.
Earth is the capital of the Federation, I cannot stress that enough, with it's biggest shipyard. There should be Starfleet vessels of all sorts of sizes there for leave, repairs, upgrades, administrative work, inspections. Just one or two crewed ships in system is shenanigans. It should be a dozen or so. Minimum. Just from Starfleet. Not including Vulcan Science Council vessels, or Andorian warships.
I mean, they might not be on full war footing or anything like that. They might be skeleton crews. But yeah, there should be a double of handful of ships in system for all sorts of reasons.
Think more major naval base that happens to be the capital on an island than anything else. It's not just a place of bureaucracy, it's a major city, and the only way to get there is by boat.
It's like more like how Venice used to be when it was a major power. Not DC.