IPA purpose seems straightforward to me: map all the known ways to produce sounds using the mouth to symbols and, for a specific language standard/dialect, map the possible sounds of it to these symbols. Now it is possible to describe the pronunciation of any word of the language/dialect in written form.
However, teachers, dictionaries and phonetic descriptions often uses phonemic transcriptions. As each phonem may be rendered by different allophones, the whole original purpose of IPA is broken IMHO.
Example 1: why use /paɪ/ instead of [pʰaɪ] to describe the pronunciation of the word "pie"? How would a Spanish native know that the initial "p" should be aspirated (Spanish has no aspirated "p")? The same applies for the flap T / D in GA English.
Example 2: GA American phonology Wikipedia shows /ɑ/ (open back unrounded vowel) as a central vowel in its vowel trapezoid diagram. Why not use the allophone [ä] instead, making clearer which is the standard sound?
The distinction between phonems and allophones may be useful in linguistics discussions, but I really do not understand its usefulness in language learning. It seems to me it only adds an extra layer of complexity and ambiguity.