That's assuming the people on the planet couldn't figure out how to continue to arm themselves. We don't really know what technological level they were at in a realistic sense. There appeared to be a smith in town and the Klingon already showed the hill people to make the weapons on their own and be self sufficient.
(Uh, just to nitpick a possible typo, weren't the hill people the folks on Kirk's side - without smiths or associated infrastructure?)
As a major plot point, our heroes discover the metallurgy of the villager flintlocks is way beyond what the culture should have. Now, perhaps the Klingons managed to teach the villagers how to make good steel. But more probably they did not, and the results would be consistent with Mao's Great Leap project: a cargo-cult approach to steelmaking, with only rudimentary quality control and not enough knowledge to bring the quality back up if deficiencies were found.
Good grade steel only emerged here on Earth after extensive manufacturing arrangements were in place (the occasional old master swordsmith being the rare exception that confirms the rule). The villagers don't seem to have mass transportation such as barges or railroads, so they wouldn't have access to distant raw materials but would have to use local sources regardless of quality. While I guess there are some odds for them being able to keep doing what the Klingons taught them for a generation or so, I wouldn't bet on them being able to keep it up past the retirement of the originally trained generation, a decade or two after the episode.
Ultimately, what Kirk did would have short-term, limited-scale repercussions - if only for the reason that the conflict we witness seems short-term and limited in scale. We are talking about small, isolated communities of just a couple of hundred people at some sort of clan warfare, without global implications because there doesn't seem to be any global infrastructure in place. Odds are, the Klingons only wanted a small foothold on the planet, and could never have hoped that their protegés would gain world dominance or anything like that. If anything, once the villagers grew too powerful for their local setting and tried to expand, people with bronze axes would hack them down by sheer superiority of numbers - unless the Klingons stayed, and taught the villagers how to
properly conquer your neighbors and keep expanding.
Timo Saloniemi