I went over to Chakoteya.net and looked up the transcription for this episode
. The writing is as gripping on the page as it is watching the live-action. TOS had one clear advantage over so much that followed, even subsequent series and movies with superior budgets: the writing was tailored to tap into your imagination more. In this age of gee-whiz CGI FX and other gimmicks, we tend to dismiss or forget that way too easily.
As far as the one scene goes where they discuss Mitchell in the Briefing Room, making the "ore ships" comment, take a gander below. The writing is superb even without the actors...
KIRK: Mister Scott, would you repeat what you just told us?
SCOTT: About an hour ago, the Bridge controls started going crazy. Levers shifting by themselves, buttons being pushed, instrument readings changing.
SPOCK: And on my monitor screen I could see Mitchell smiling each time it happened, as if this ship and crew were almost a toy for his amusement.
KIRK: Are they right, Doctor? Has he shown abilities of such magnitude?
DEHNER: I saw some such indications.
KIRK: And you didn't think it worth mentioning?
DEHNER: No one's been hurt, have they?! Don't you understand?! A mutated superior man could also be a wonderful thing! The forerunner of a new and better kind of human being!
KIRK: Mister Sulu.
SULU: If you want the mathematics of this, Mitchell's ability is increasing geometrically. That is, like having a penny, doubling it every day. In a month, you'll be a millionaire.
SPOCK: In less time than that, he will have attained powers we can't understand and can't cope with. Soon we'll be not only useless to him, but actually an annoyance.
KIRK: There'll be no discussion of this with the crew. Thank you. (everyone but Kirk and Spock leaves)
SPOCK: We'll never reach an Earth base with him aboard, Jim. You heard the mathematics of it. In a month he'll have as much in common with us as we'd have with a ship full of white mice.
KIRK: I need a recommendation, Spock, not vague warnings.
SPOCK: Recommendation one. There's a planet a few light days away from here. Delta Vega. It has a lithium cracking station. We may be able to adapt some of its power packs to our engines.
KIRK: And if we can't? We'll be trapped in orbit there. We haven't enough power to blast back out.
SPOCK: It is the only possible way to get Mitchell off this ship.
KIRK: If you mean strand Mitchell there, I won't do it!!! That station is fully automated. There's not a soul on the whole planet. Even the ore ships call only once every twenty years!
SPOCK: Then you have one other choice. Kill Mitchell while you still can.
KIRK: Get out of here!
SPOCK: It is your only other choice, assuming you make it while you still have time.
KIRK: Will you try for one moment to feel, at least act like you've got a heart? We're talking about Gary!
SPOCK: The captain of the Valiant probably felt the same way, and he waited too long to make his decision. I think we've both guessed that.
KIRK: Set course for Delta Vega.
NEXT SCENE: ENTERPRISE APPROCHES PLANET DELTA VEGA
Star date 1313.1. We're now approaching Delta Vega. Course set for a standard orbit. This planet, completely uninhabited, is slightly smaller than Earth. Desolate, but rich in crystal and minerals. Kelso's task, transport down with a repair party, try to regenerate the main engines, save the ship. Our task, transport down a man I've known for fifteen years, and if we're successful, maroon him there.
I realize that final transcription of the live-action TV show is almost never identical to what we originally written, but what the actors portray is obviously an evolution of that. Gripping drama, to be sure.
As for the logic behind what Delta Vega appears to be, that's always been curious to me. We must remember that what Delta Vega represents to us is as much based on imagination as anything else in this wonderful story.
Kirk's statements about the planet, including the narrative, seem to strongly suggest that the planet supports some kind of mining operation, supposedly for extremely rare minerals. The presence of an automated station there strongly suggests a robotic mineral extraction operation of some kind.
Of course, in order to make the establishment of any kind of outpost make sense, whatever it produces would have to be unusually valuable. If this automated "lithium cracking station" produces useful dilithium crystals, often touted as the invaluable heart of starship technology, then a distant source such as this would likely be an important claim.
We are told the station is automated, but we never really see anything other than a reasonably clean facility that appears to be well-kept. On a lifeless planet, one that seems to have little or no consistent rainfall, it may be fairly easy to set up an automated system of computer server farms, robots, radio telemetry and backup systems to keep everything "ship shape". Obviously if "the ore ships" come for a pickup only once "every twenty years", the facility's robots must take that long to extract and purify enough dilithium (or whatever else) to make the trip worth it. Still, we are talking about sending starships into deep space-- the galaxy's edge --to retrieve some mineral content. That content would have to be mighty valuable.
Since a term like "Delta Vega" usually refers to a star or stellar system in TOS, we can assume that this planet is the only one with breathable atmosphere in this entire region. (Strange how a lifeless world would have such an atmosphere; oxygen would seem to suggest some kind of life, even if its just oceanic plankton or plant life on land. Stranger still that the planet would be chosen for a mining facility; if there are no other "class m" worlds in the region, it would seem ideal for colonization)
The notion of a full-featured facility, complete with a dispensory/sickbay and a brig, is interesting for an uninhabited world. I see two possibilities: (1: the "cracking station" is set-up as part of a prefab kit that was built many light-years away, hauled out to Delta Vega via warptug, and plopped down at a specified location that a geology/exploration operation designed it for... either that, or a much smaller robotic package was sent there, and the robots built the facility on-site out of locally mined materials, either from the planet or from nearby asteroids... or... (2: a colonization expedition was dispatched here shortly after the Valiant left Earth (maybe a probe discovered the planet and found it to be habitable), so the expedition started to build a colony, discovered minerals of extreme value, but found the planet to not be as attractive to live on as they hoped; maybe the disappearance of the Valiant or some other activity made them think it wasn't safe to live here, so they converted the colony to automation and left.
I prefer to think that either United Earth or some joint coalition of planets sent out a collapsed prefab robot facility on a warptug, and that facility just plopped itself down and started working. The facility contained full-featured living quarters in case a visiting starship's crew needed a little shore leave or repairs. Maybe the brig was included in case the Valiant was lost to local pirates. After all, if you catch a pirate, you gotta have some place to incarcerate him!