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The English language has the diphthongs /eɪ aɪ ɔɪ aʊ əʊ/, analysed differently in some accents. They end in sounds that are very close to [j] and [w], yet are analysed as unsyllabic [ɪ] and [ʊ]. Since they sound and act almost the same, especially before another vowel, I think that it just makes a lot more sense to just analyse it as these semi-vowels. I see some analyses do treat diphthongs this way, but surprisingly few. I wonder what keeps people from doing so.

In fact, to take out even further, I would analyse the preceding vowels as existing vowels, since all are practically identical to one except [a], which is close enough to /æ/ in most British accents (an alternative could be /ʌ/ which is very close in most pronunciations). It seems like people are just resisting rather simple ways to simplify the English language. Are there any good reasons for this?

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There are certainly authors that analyze English diphthongs as vowel + glide, but as far as I understand the primary reason they are widely analyzed as distinct phonemes is that /j, w/ are otherwise not found in syllable codas (in other words, [a, ɔ]—and [e, o/ə] if you include FACE/GOAT—appear to be the only vowels that can precede a glide within syllables). The analysis with diphthongs also seems to allow easier explanations of historical developments and dialectal variation, like the fact /aɪ/ derives from ME /iː/ and gets monophthongized in Southern American English.

(Also note that in North America FACE and GOAT are commonly analyzed as monophthongs /e, o/ on the grounds that the gliding is no greater than that in FLEECE or GOOSE, which conversely means it is also possible to analyze the latter as /ɪj, ʊw/.)

Wells (1982: 49–50) justifies his analysis as follows:

Depending on the accent we are investigating, there may be phonetic grounds for identifying [the nucleus of PRICE] with the vowel of palm, that of strut, or that of trap; but in some cases – in RP, for instance – it is phonetically different from all three of these, occupying an intermediate position. Hence the biphonemic interpretation is faced with the arbitrary choice between /ɑːj/, /ʌj/, and /æj/ as a phonemicization of [aɪ]. Similar difficulties arise with the [ɜʊ ~ oʊ ~ eʊ] of goat in RP and similar accents: ... is the first element to be identified with the /ə/ of comma, the /ʌ/ of stut, the /ɜː/ of nurse, or even the /ɒ/ of lot or the /ɔː/ of thought? ... A biphonemic analysis of diphthongs forces the analyst to make many such difficult – and essentially meaningless – choices. ... [The monophonemic analysis] is further supported by diachronic considerations ...

And Cruttenden (2014: 99–100):

(1) they do not have a distribution after all vocalic elements as general as that which we find in the case of /j, w/ preceding vowels;

(2) they are in [General British] very weakly articulated (compared with pre-vocalic /j,w/) and may correspond to monophthongal pronunciations in many other accents, e.g. /eɪ/ may be [eː] or [ɛː];

(3) they have none of the devoiced fricative soundings characteristic of /j, w/ following /p, t, k/, e.g. in tune and queen.

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    The fact that /j w/ don’t otherwise appear in codas seems rather circular. Given that the diphthongs cover all possible examples of coda /j w/, you’d expect nothing else. The fact that combinations like /rw lj tw mj/ do not appear in coda position doesn’t say much, unless you consider there should be some reason why they should, despite violating the sonority principle. Even in languages where diphthongs are regular considered to be sequences of vowel + glide, /j w/ frequently don’t appear in coda position except as part of a diphthong. May 1, 2022 at 15:21
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    The circular criticism indeed occurred to me, but my point is that the vowels that can precede a glide would seem unusually limited if you exclude phonemic diphthongs.
    – Nardog
    May 1, 2022 at 15:51
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The Sound Pattern of English, Chomsky & Halle (1968), treats diphthongs as sequences of vowel plus glide. One reason for this treatment is that there is a difference between [əɪ] and e.g. [ey], for example Judaism [əɪ] vs. daily [ey] ([ej] in IPA transcription). This postvocalic glides are introduced in §4.1 by rule after tense vowels, by rule (21). A fair amount of that work is dedicated to removing segments from underlying forms, therefore they eliminate all diphthongs from underlying forms, and make them be the epiphenomenal result of rules applying to more abstract representations (for example, tense vs. lax vowel, including the cases of [ai, au, oi]).

The theoretical driving force here is "capturing generalizations" (we all agree that valid generalizations should be captured, we don't agree on what a valid generalization is). Under their metatheory, if some combinatorially-possible arrangement of segments is non-existent in the data, that has to be the result of the rule system. They have rules that prohibit underlying forms with pre-consonantal glides, and they have rules and representations that account for all output examples of pre-consonantal glides, so they have captured a generalization which says that there aren't any words like *[bɪwn] in English, which would otherwise be possible given free combination of elements.

The arguments that they posit lose force once the theory also embraces the concept of "syllable" (not part of SPE theory), which then enabled alternative analyses of daily as one of [deili, dɛili, dɛɪli, dɛɪli]. A second factor that lead to the broader acceptance of such competing representations was the acceptance of a separate phonetic component (in SPE, phonology generates the phonetic output which is presented to the articulatory apparatus and is executed language-invariantly). Where SPE was committed to a more-phonetic phonology, later theories embraced greater abstractness in the phonology (though at the same time rejected certain kinds of abstractness such as /œ̄/ as the underlying form of oi).

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