but the butterfly effect is a huge thing in reality.
Is it? It might be, if time travel existed.
It's theoretically possible, but that doesn't even matter. It matters in terms of the multiverse, and in terms of the linear existence of this universe. History isn't really set out; it's all a random assortment of causes and effects with every tiny detail which builds up to make a larger picture. It's like a beach; the beach is an illusion, and all it really is is a collection of sand. And little disturbances completely shift the grains of that sand.
Or in other terms, if you rewound history and allowed it to play out an infinite number of times, it'd be different each time regardless. It doesn't take a time traveler interfering. Just pay attention to where your day started out and ended, and how many things could have gone totally differently; and that leads into a week, a month, a year, and you increasingly deviate from any number of alternative actions and outcomes that could have come about. It wouldn't be a different day between two different realities in the multiverse wouldn't seem all that great, but take the point of departure from that one day, and jump ahead a year and compare those two universe and they'd be totally different, not to mention the countless alternatives which would have lead to infinite further alternate realities.
So in terms of even just the reality you can see, the butterfly effect is huge.
That being said...it is an animated television show from the 70s. It doesn't matter what the logistics may hold, because the logistics of the narrative can be different and are whatever the writer wants them to be. But it is an interesting thought.
I understand your point, but then you're backing off a bit at the end by saying it's just a show.
I think it's pretty clear the ripple effect is demonstrated in the episode by when Spock didn't save himself. So it's not that the effect isn't portrayed, it is.
But really, while possiblities abound, what or who really would have been changed by I Chaya dying a few years earlier. (I think it's safe to assume the animal is long dead when mentioned in Journey to Babel, it was supposed to be old in the animated episode) Would Sarek have become more logical? Would Amanda have a harder time pronouncing her name?
I'm picking minor things at random but there could have been something more major, maybe I Chaya could have been stubborn one morning, held Sarek up by wanting to be petted and he is injured in a transportation accident, which prevents him from attending the Babel confrence, he is not there to argue Coridan's admission to the Federation, then an Orion/Tellarite alliance seceed from the Federation weakening it sufficiently that the Romulans can attack and destroy stuff, at this point it's not necessary to continue.
So I see your point, his death could have had a huge impact, but it didn't have a huge impact on "the universe" It only had a huge impact on Spock, which I think was the theme of the episode, the needs of the many outweigh the needs of yourself and compassion for other's condition.
Maybe the death experienced at an earlier age is what drove Spock to learn the Kohlinar, we really don't see anything about Spock between the last of the Animated series and The Motion Picture. I saw no indication that Spock would want to leave Starfleet when he was there like TMP showed. Also, because of the episodic, multiple writers nature of the show, no marked emotional change could be depicted in any meaningful way, but I think it was intended by Nimoy's delivery of the final scene.
So, continuing my little fantasy, if I Chaya did survive to die of old age when Spock was a "teenager" then Spock may not have felt the need to attempt Kohlinar to purge all emotions because the trauma of an old pet dying for a teen is not as bad as being killed while much younger. Taking this indulgence further, Spock wouldn't have been in Kohlinar if IChaya lived longer and then wouldn't have been in the same "mindset" as V'ger and Earth and the Enterprise would have been destroyed.
I think just because the effect isn't immediately visible doesn't mean it isn't there. Sorry for the long post.