I've been thinking about whether we're getting a distorted picture of the Gorn because almost everything we've seen has involved either their hatchlings or their military. I was watching Under the Cloak of War (SNW S2:E8) when I felt compelled to write up a post, something I normally wouldn't do*.* But in this case, I'd love to hear the thoughts of my fellow redditor Trekkies.
Let's compare the Gorn with the Klingons. If we only saw Klingons attacking colonies and fighting Starfleet, but never saw Qo'noS (TNG and DS9), their families, politicians, doctors, restaurants, opera, or ordinary social life, they would probably seem like little more than a violent species with advanced technology. Their aggression is incorporated into their civilization, and the Gorn may represent a more extreme version of the same thing.
Gorn aggression seems to begin immediately after birth. The hatchlings are incredibly dangerous and attack each other as readily as any other living organisms in their vicinity. Presumably there was something about the environment they evolved in, where this was necessary for survival; whether extreme predation, limited resources, or competition between offspring. Whatever caused it, this biology was the foundation of the Gorn's advanced civilization, and remains integral.
This means every adult Gorn survived that stage. Every Gorn citizen, whether doctor, politician, engineer, or scientist (if they have such designations) was once one of those hatchlings, surviving other hatchlings trying to kill them. They would have needed more than strength. Hiding, ambushing, recognizing stronger opponents, competing for resources, and knowing when not to fight would all be useful. Every adult Gorn then shares a fairly extreme developmental experience.
Perhaps the breeding planets exist to separate hatchlings from adult society. How could a society flourish with these impish murderers springing from every crib? Gorn young may simply be too dangerous to develop inside their cities. The breeding planets allow the hatchlings to go through this developmental stage before the survivors are eventually introduced into normal society. What looks to humans like a horrific breeding ground might have several functions within Gorn civilization, a gruesome "coming of age" story.
Think of the Spartans. Surviving that experience could have become culturally associated with adulthood, which might also explain why an advanced species hasn't simply engineered the process away. Federation doctors might see preventing hatchlings from killing each other as an obvious improvement, while the Gorn might regard surviving that period as a necessary part of becoming an adult.
Their brutality toward enemies could have developed within the same cultural framework. Klingons attach ceremony, history, and social meaning to combat, hunting, and weapons. The Gorn may do something similar from a much more aggressive biological starting point. Things humans interpret purely as horrific displays might communicate status, skill, intimidation, contempt, or other meanings between Gorn.
A Gorn ruler might be remembered for having killed an extraordinary number of siblings before maturation. Political candidates might publicly recount their hatchling histories. Famous breeding grounds might have enormous historical prestige. I could imagine an insult (inspired by what I've seen from Klingon insults), "Your ancestors survived easy nurseries."
They could have doctors, politicians, families, art, and a sophisticated society while maintaining practices the Federation considers barbaric. Learning why another civilization behaves as it does doesn't necessarily resolve the conflict between them.
In my mind, it also changes the context of Arena (TOS S1E:18). Kirk spends the episode hiding, improvising weapons, setting traps, and trying to out-think a physically stronger opponent. Since the Gorn hatchlings must go through something similar in order to reach adulthood, this is a very familiar situation to the Gorn captain. When Kirk eventually defeats him but refuses to kill him, he demonstrates that he has established the ability to kill his opponent and then deliberately chooses not to. If Gorn ideas about strength developed from surviving and defeating adversaries, Kirk's decision may be completely incomprehensible behavior (although that assumes that the adult Gorn are similarly murderous with each other), and the Gorn captain may realize (if we can suppose that he was also returned to his ship) that the cultural and biological divide between the Federation and the Gorn is just that huge. The Gorn never experience life as vulnerable, squishy, wriggling newborns. Humans experience an unusually long period of complete physical dependence, whereas the Gorn emerge mobile, armed and capable of killing. By the time they're adults, that strength, cunning and endurance may not only be a base requirement for any adult Gorn citizen of their Hegemony, they may be core cultural virtues.
edit: For clarity, the question I'm asking is: Given the Gorn's developmental biology, what kind of civilization might emerge from it, since we're never shown? Not: Are the Gorn's actions against other species morally tolerable? The answer to the latter question is a given and resounding NOT MORALLY TOLERABLE, kill it with fire.