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?
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.