There are camps that say tritype is not necessary -- I find that depends on what you're looking for. Even with Jungian functions, I find that you can nuance farther and farther, and use the language of the functions indefinitely to find subtle differences between people beyond those suggested at the higher level of just 16 or 8 types.
My main problem with many tritype-ain't-needed camps is they seem to be reacting to the Fauvres system and comparing it to a more Naranjo-like system, and to me this is apples and oranges, because the Fauvres system still seems resembling of the test/RHETI, and is more trait-theoretic. Understandably, someone encountering such a framework may think that pasting a lot of traits together in an unstructured way is not so enlightening.
However, the IDEA that the ego will always be faced with the questions of head, heart, and gut is to me pretty hard to shake off. I'm not sure if it merits pinning down one single type for each of the three, but the idea isn't answered by responses like "you can just use the lines of integration/disintegration".
I think what's clear is different versions of each core type exist, and the only question is whether these differences can be explained by the reactions people have to other centers.
I'd lean that there's some merit to that.
I mean, let's say someone is a 1. They have a 2-wing and a 4 line. Does that cover the interactions 1 has with heart themes? Not necessarily at all. The lines and wings all cover relations type 1 has with other types. A line is similar to an axis in functions theory: Ni/Se are related by the tenet of being complementary views on the irrational side of cognition. But, 1 and 3 are both competence-seeking types. They thus share a relation. Is it possible someone with a competence-seeking motivation endowed by core 1 may supplement that competence-seeking with some 3-ish drives?
If not, why not get rid of wings too? Why not say whatever 2-ishness you see in a 1 is just because 1 neighbors 2, and it's useless to pick out wings? If we can say some 1s seem genuinely more 2-ish, why not say some 6-ish seem to be the greatest self-doubting types, more so than other 6s and have some 9 influence? Now, some will say, but that's because some are p and some are cp...some are sp...some are sx. Sorry, but why is sp ~ self-doubting in a type 6? Overall, I've not found the explanations satisfactory, and find the subtypes sp/sx/so of Naranjo just as arbitrary as tritypes, and honestly I think either just stop creating subtype systems and admit there are just various varieties of each core type or be flexible with what subtype system you allow. Tritype is really a subtype system.
My general answer is that you can focus on core, but realize part of that is picking out the many varieties/subtypes of a type, and I'm not sure there's a canonical reason to stop at the instinctual subtypes commonly presented. Whether you refer to a formal tritype or not, keep in mind the answers you have to the other triads' questions when figuring out your core, and you'll 'already' have done the work of finding a sort of tritype.
But the idea wasn't to argue that the core type should be everything there is in a person. It was more or less the opposite - questioning the need for pumping up a theory with different kind of applications so it would be waterproof - instead of being a platform for introspection. That's why I wondered if tritype was just "an application" of Enneagram. GavinElster's post was therefore very informative, thank you
