This is really more a comment on Jknappen's answer, but it's too long. A premise of the IPA is that each symbol is a sound that is a contrastive phoneme is some language. The letter "i" represents a general area of the vowel space, which overlaps the space of adjacent vowel somewhat (especially "ɪ"). If you look at a range of IPA illustrations, you will note that the vowel positions vary within the vowel frame depending on language. The position of the vowel in the vowel frame is more informative than the letter used, but that spacing obviously can't be included in a transcription. Ideally, this positioning would be based on measured mean formant values, but typically they are based on subjective evaluation. Usually, the convention is to select the IPA letter that is closest to the perceived location of the given language's instance of the vowel, but you can pick a different symbol either for phonological reasons ('it acts like a front vowel') or typographical reasons ('why not just use "a"? How do you even type "ɐ"?').
In order to reduce all phonetic vowel differences to single letters, an enormous set of distinct symbols would be necessary, since there are dozens of known kinds of "i", likewise "ɪ", "e", "ɛ" and so on.