Kolos also spoke of his parents, a father who was a teacher and a mother who was a biologist, who were from a generation that encouraged him to pursue law, whereas by the time of "Judgement" the warrior class had become dominant.
In The Troubble with Tribbles, there was this:
... one side or the other must prove it can develop the planet most efficiently.
... And unfortunately, though the Klingons are brutal and aggressive, they are most efficient.
It's hard to see warriors "developing a planet," so other aspect of the Klingon culture do exist, along side the warriors.
In the Houses of Quark, it's revealed that the various Klingon aristocratic houses have complex property, financial and trade dealings with each other. Again, not simply warriors.
Given the strength and (presumed) size of the Klingon Empire, would it really be the Empire joining
the Federation? Or would you see instead more of a merging of the two into a whole? Why would the Empire with hundreds of star systems become a member of the Federation council where they are on equal footing with species/races than have only a single planet?
The Federation might be more inclined to merge with the Empire if the Federation itself were in some kind of desperate straits, and were ready to "lower their standards."