An example of how your core type's motivations influences everything from thought to physical behavior is how the 4 has a tendency for intellectual interests, artistic snobbery, indulgence in sensual experiences, and using their physical image for self-expression. Their image drive affects how they think, feel, act and appear.
I understand this argument, and I'm not discounting it, but it also doesn't explain away the possibility that it's simply different ways of describing the same traits. For instance, not to re-type you (as I don't know you), but what if instead of not being a standard melancholy 4w3, a person was really a 3w4, still in the image triad but more likely to suppress emotions to move towards image-goals, rather than lingering in emotions to amplify an identity rooted in them? That's just a hypothetical example of how there different ways of explaining personality traits in enneagram, and how it may be a matter of anything from wing influence, directions of growth, and even mistyping due to lookalike combinations. It should be noted that many enneagram theories note that types are influenced by BOTH wings, but that one tends to be stronger. So you have dimension as well....For example, I'm a 479, my life's biggest problems personality wise root from seeking my identity - that is my core. However the 7 and the 9 help explain the other parts of my personality, and saying that I'm a 479 ultimately gives a fuller explanation of who I am than just saying I'm a 4. Maybe I just find tritypes more convincing because I'm a 4w3; meaning that both my type and my wing are in the image fix. It's easier for someone like a 4w5 to find that title useful, there's already a number in 2 different fixes (though that can be misleading of course). If your wing happens to be your second fix, you're super lucky. For a guy like me however, tritypes explain a lot. I doubt I can last a week in the weeping melancholy of a standard 4.