Why's IPA constrainted by phonemic, not phonetic, contrastivity?

Question

To try to understand phonetics vs. phonology, I already read What's the difference between phonetics and phonology?, Oxford Univ. Prof. John Coleman's page, ResearchGate, Univ. of Pennsylvania Linguistics, Quora, SUNY at Albany's summary.

Please see the "phonemic" that I colored in gray. If the author wrote "phonetic", would that sentence still be correct? Why didn't the author write "phonetic"?

14.1 Phonetic, Semantic, and Glottographic Writing

Language is a relationship between sound and meaning, and it contacts the real world at two interfaces; phonetic and semantic. In principle, we can represent an utterance by writing at any of these three levels: phonetic, linguistic, or semantic.
      We are familiar with the notion of a phonetic writing system which could be used to transcribe the sounds of any utterance in any language in the world; such a system would be similar to the International Phonetic Alphabet (IPA; see Appendix B and International Phonetic Association 1999), which provides an inventory of symbols for a wide variety of phonetic phenomena which occur in human speech with certain rules for using these symbols. The symbols represent pure sound and are not associated with any particular language. That is, the IPA provides symbols sufficient to represent all those phonetic distinctions which are contrastive in some language somewhere. However, as MacMahon (1996) notes: 'Strictly speaking, then, the IPA is not a universal phonetic alphabet in the sense of an alphabet that will provide a notation for every conceivable sound used in a natural language. Rather, it is a selective phonetic alphabet which is constrained by the requirement of phonemic contrastivity.' Even though the IPA may not be a completely phonetic writing system, it is clearly a close approximation.

Henry Rogers, Writing Systems (2004), p 269.

Answer 1

"[A]n alphabet that will provide a notation for every conceivable sound used in a natural language" will require an infinite number of letters because every sound in every utterance spoken by every person in every language is different. So any practical system of representation of spoken language will have to make a choice on what aspects of sounds to represent, create a finite number of categories based on that decision, and throw those infinitely variable sounds into those categories.

So, for starters, the IPA does away with all information that is not "linguistically relevant", as the Handbook of the IPA (1999: 4) puts it, "such as 'spoken rapidly by a deep, hoarse, male voice'" (although systems to augment the IPA for such aspects of speech have been created, chiefly for speech pathology).

Even still, there are infinite shades of sounds between each pair of adjacent places of articulation, e.g. [s] and [ʃ], as becomes obvious if you move the tongue back and forth while articulating one or the other. So you have to draw a line somewhere, or you'd need an infinite number of letters again. So the IPA turns to "phonemic contrastivity".

The IPA arose from language teachers' desire to describe sounds in languages of western Europe to students, and to write them down, in a consistent way in the late 19th century. They first had a different system for each language, but this quickly became confusing, so they decided to make a uniform system, under these principles:

1. There should be a separate sign for each distinctive sound; that is, for each sound which, being used instead of another, in the same language, can change the meaning of a word.
2. When any sound is found in several languages, the same sign should be used in all. This applies also to very similar shades of sound. [...]

A "sound which, being used instead of another, in the same language, can change the meaning of a word" is what we now call a phoneme. Obviously languages draw those lines differently, and there are needs to describe non-phonemic differences of sounds, so the IPA now has a number of letters and diacritics it didn't when it was first conceived, but principles similar to the ones above still dictate what goes in to the alphabet and how the value of each letter is defined.