There's another angle to consider. We don't know everything about the Delta Vega facility, since we only see one exterior view and a few limited interior views of it. I don't see anything to establish that it's just a planetside mining facility only. The facility looks large enough that it could support interplanetary robot ships that could mine asteroids for needed materials.
I like Timo
's "Project Vega" logistical chain suggestion. Delta Vega could be an outpost to support future outward expansion, perhaps established at a time when starships capable of high-warp speeds was still a dream for Earth. Delta Vega itself represents one of those facets of the STAR TREK Universe, especially the TOS Universe, where we are left to our imagination. We don't see any robots, but we're told the facility is "completely automated; there's not a soul on the whole planet", and yet there's a fully featured, ready-made facility, obviously well-kept and built to accommodate people for an unknown duration on a planet that's described as "uninhabited" and "desolate". To me, this speaks volumes about what Roddenberry and company seemed to expect of the engineering and building capabilities of Earth and allies in the far future. They must have awe-inspiring abilities to be able to not just build faster-than-light starships but also to haul themselves thousands of light-years to build such an excellent station on an isolated frontier, where "even the ore ships call only once every twenty years".
The only things that make me scratch my head: (1: how did this uninhabited, apparently desert world get an oxygen atmosphere, (2: if the facility is totally automated, does that mean there are all these robots like Flint's M4 floating around, just out of sight of the show's characters, or maybe Robbie the Robot, or the Jupiter II Robot, and (3: how were the Delta Vega "power packs" adapted to "regenerate" the Enterprise's engines.
I do have another alternative theory about the Delta Vega station. It could be that Kelso and his crew actually whipped up much of what we saw (the brig, suggestions of a "dispensory", the control room where Kelso was killed) out of kits aboard the Enterprise, simply salvaging cruder, abandoned facilities that were left there by a previous ship. It could be that deep space craft carry "clean up the station and leave it better than you found it" kits for contingencies like this.