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You don’t have to build a whole ring. You just need a boom and a counterweight.
I guess the hard part would be that a truncated-circle-sector-shaped room is more awkward to launch than a rocket-section-shaped one of equivalent usable space. (Also, you need a tube and a ladder down to a docking port at the center of mass, because spaceships can’t line up with a target swinging through an arc.)
You climb up to the center, not down.