What is the rationale for considering di-, tri- &co. -phthongs separate entities? Why aren't these sounds interpreted as sequences of a vowel and a glide? How would be linguistics deficient if aliens came to Earth to erase the term from everyone's memory?
(I am interested in both, the historical reasons (Latin or Greek grammarians, I suppose?), and the modern rationale for continuing to use the term.)
It is useful to define a linguistic unit when there is evidence that some linguistic process is sensitive to that unit. For example, phonologists and phoneticians have long recognized that the concept of a syllable is a useful one due to evidence from scansion in poetry, syllable-final devoicing, processes related to stress and tone, phrase- and utterance-final syllable lengthening processes, etc.
Similarly, there are many processes that are easiest to describe when we are able to make reference to a diphthong as a unit. In "English Phonology", John Tillotson Jensen raises three sources of evidence for the diphthong as a unit in English:
In addition, it is common to observe dialectal differences that revolve around diphthongs. For example, in many dialects of English spoken in the south of the U.S., the /aj/ diphthong is "monophthongized" and produced as [aː] (where [ː] is the symbol for "long"). It makes sense to think of this phenomenon as monophthongization as opposed to "glide dropping" because those same speakers still produce the /j/ glide as [j] elsewhere, including after /a/ (i.e. a speaker that says [aː.ɛs] for I.S. will still say [aː.jɛs] for ah yes).
I'll concentrate on the historical part of your question as others are doing well on the modern work. As you've suspected from the etymology, the term δίφθογγος is Ancient Greek (diphthongos, borrowed into LL as diphthongus) and was already in broad use by the 2nd century CE - e.g., Terentianus writes:
Porro vocalem secuta vim tenet vocalium
Et sonos utrosque jungit, unde diphthongos eas
Græciæ dicunt magistri, quod duæ junctæ simul
Syllabam sonant in unamMoreover the following vowel has the force of a vowel
And joins both sounds; whence the diphthong,
The Greek masters say: the two joined together
Sound as one syllable.
...and just as old are arguments about it. Is the diphthong two, or is it one? Is it a single sound regarded as a unit, or two sounds yoked together? Pennington's 1844 An Essay on the Pronunciation of the Greek Language reveals this term has provoked long disagreement since classical times.
Now, because there has been a single term for the diphthong, we can say that it has been regarded as a single entity (of some type) since classical times, though its nature has been disputed. The ancients did know that a diphthong was sounded in a single syllable; they typically regarded as the syllable as the smallest unit of sound. So I think that our own usage today of diphthong as being in some sense a 'single sound' is a relic (correct or incorrect, as others discuss) of that time.
Outside of the dominant 'Phoneme Theory' in Phonology there are other explanations out there (gaining ground I believe) such as 'Element Theory' and in this theory, these would not be considered individual units at all. Just so you know not 'all' models of Phonological Theory subscribe to this notion.
