The only purpose that the 4 letters really serve are to point to the 8 functions, which are the real indicator of type.
Carl Jung — mystical streak notwithstanding — was a believer in the scientific approach, and Isabel Myers took Psychological Types and devoted a substantial chunk of her life to putting its typological concepts to the test in a way that Jung never had, and in accordance with the psychometric standards applicable to the science of personality.
And among the things that Myers discovered — despite some lip service to the functions — is that the dichotomies are really what type is about. And as James Reynierse has (rightly) noted, 50 more years of MBTI-related data has very much confirmed the correctness of Myers's dichotomy-centric perspective, and strongly suggests that the proper characterization of the so-called "cognitive functions" is that they're essentially what Reynierse calls a "category mistake."
What's more, and contrary to the notion that a function-centric perspective offers more richness and depth than a (properly framed) dichotomy-centric perspective, it's actually the dichotomy-centric perspective that's richer and more flexible — in part because, as Myers understood, all the dichotomy combinations correspond to noteworthy aspects of personality. Myers thought the most meaningful preference combinations were ST, SF, NT and NF (each of which includes four types with four different dominant functions), and she may or may not have been right about that (Keirsey certainly disagreed) — but she correctly understood that there was nothing particularly special about the combinations that purportedly correspond to the functions.
If you're interested in reading a lot more about the INFP=Fi-Ne-Si-Te model — a function stack that's inconsistent with both Jung and Myers and has never been endorsed by the official MBTI folks — and about the relationship between the dichotomies and the functions, the place of the functions (or lack thereof) in the MBTI's history, and the tremendous gap between the dichotomies and the functions in terms of scientific respectability, you can find a lot of potentially eye-opening discussion in this post and the posts linked to in its last two paragraphs.