Kirk takes charge
Here are a few problems with the episode:
The Federation supposedly was founded by humans, Vulcans, Andorians, and Tellarites. How many times did we see Vulcans, Andorians, and Tellarites in positions of Federation authority? How many times did they give orders to humans? Once or twice in the 79-episode history of TOS, at most.
It's as if Kirk chose which wife and child of King Henry VIII should form the ruling house of England. Rarely if ever have the Federation's people violated the Prime Directive so egregiously.
These Capellans were only obeying their leader's orders, enforcing their culture' laws. But Kirk and Spock clearly think their right to be free supersedes the Capellans' right to live. They react to the Capellans as if they're animals.
Moreover, the Capellans never developed the bow and arrow. Kirk has introduced a dangerous and destabilizing new technology to them, another massive Prime Directive violation.
Clearly these savage
What would happen if Kirk and the Federation didn't get their way? We saw an example of that in Errand of Mercy. Kirk couldn't conceive of the Organians not wanting to cooperate with the Federation. He was ready to go to war rather than let the Organians live in peace.
Yes, he thought the Klingons would take over Organia. But the Organians made it clear they were choosing noninterference. Kirk had no right to say, "We know better than you, so you must follow our lead."
Has an alien species ever simply refused to have contact with the Federation? In the ST novels, surely, but in the TV series? I think there were some in TNG, but some emergency inevitably compelled contact. After that, Picard and company's openness and goodness inevitably convinced the aliens to change their ways.
For more on the subject, see White Super-Race in Paradise Syndrome and Noble Savages in Paradise Syndrome.
P.S. The novel Ghost-Walker by Barbara Hambly may be the best exploration of colonialist issues I've seen in an ST novel. Check it out if you're interested.