/ɪə/, /eə/, /ʊə/ as phonemes?
From what I understand on phonetics/phonology, /ɪə/, /eə/, /ʊə/ can simply be considered as allophones of /ɪr/, /er/, /ʊr/, but most traditional dictionaries treat them as distinct phonemes. Is that just a learners' dictionary thing (to denote the clear phonetic differences between major dialects, rhotic or not, etc.) for the sake of convenience or is it legitimately phonolocal?
Solution 1:
There is a contrast (in most non-rhotic varieties of English) between words like "ferry" /feri/ and "fairy" /feəri/. How should we analyse them if /eə/ = /er/? As /feri/ and /ferri/? That doesn't seem right to most people. Perhaps you could use syllabification (/fe.ri/ vs. /fer.i/), but people don't really agree about how to syllabify words like "ferry."
Another reason for the r-less notation is for parallelism with the notation of two other phonemes that can correspond to rhotic vowels in rhotic Englishes: /ɑː/ (START lexical set) and /ɔː/ (NORTH and FORCE lexical sets).
Since /ɑː/ and /ɔː/ in non-rhotic dialects also have other origins than vowels historically followed by r (the BATH and PALM lexical sets, and the THOUGHT lexical set), we can't analyze them as /ɑr/ and /ɔr/, unless you want to say that words like bath [bɑːθ] and caught [kɔːt] have somehow undergone a phonological shift that added the phoneme /r/ after the vowel. (Most phonologists do not want to say this.)
The sounds [ɪə] and [ʊə] can also arise in some dialects from sequences that lack historical /r/ by way of vowel coalescence (in words like idea), so the same issue of historical development applies there.
Solution 2:
In most American dialects, /ɪər/, /eər/, /ʊər/ are allophones of /ɪr/, /er/, /ʊr/. Some speakers say /nɪər/ (near), but /nɪrər/ (nearer) and /mɪrər/ (mirror). So if you speak one of these dialects (or are learning English from somebody who does), this distinction may be confusing.
Dictionaries make these distinctions because they exist for many speakers. In the U.S. Northeast, many people (both rhotic and non-rhotic speakers) still make these distinctions, and outside of North America, they are hardly ever allophones.