The basic phonetic property explaining this rareness is that the sounds are too similar. You can add to the list things like [iɪ], [ɛe] and so on, where there is also just a subtle shift in F1 or F2 frequency. Essentially, you have to be paying a lot more attention to detect the small and relatively brief shift in formants in such diphthongs, which means that they are less likely to develop historically. They do get started (assuming we're at the historical state where such diphthings are first coming into existence in a language), and if they are aren't further distinguished by other some development (uw → ɨw) then whatever is causing diphthongization in the first place is likely to be suppressed in these cases.
"Two closed vowels with the same roundness" means that these are purely backness -changing diphthongs, which means that the components are acoustically almost the same. The primary acoustic correlate of backness is F2, which is also the primary correlate of rounding (which is why back vowels tend to be round and front vowels tend to be non-round). Backness-shifting diphthongs will therefore have only a very subtle shift in formants that requires bringing in higher formants to tease out the contribution of rounding vs. backing.
An example of roundness dissimilation (in a height diphthong) is that general North Saami uo e.g. guokta "2" becomes ue i.e. guekta in the Kárášjohka dialect. Various dialects of English have this as well, so that /u:/ which is generally pronounced as [ʊw] in the US is often further shifted to [ɪw] (California speech and younger speakers are two high points of this trend).
Analyzing diphthongs with the completely same vocoid features is tricky, since analysis is often smuggled into the transcription. The specific issue is whether one has a glide plus vowel sequence as implied by transcribing , versus a two-vowel (one-syllable) sequence as implied by . There certainly are languages that have "wu" and "wu" can even contrast with [u:], and that is a context where it is certainly appropriate to transcribe the "diphthong" as a glide plus vowel sequence. In onset position, the glides [w,j] are much more constricted and it is easier to parse the glide as a separate phoneme. It is typical to not analyse "wu" and the like as a diphthong, and in every language that I know of with "diphthongs" so transcribed, they behave as CV... syllables, not as VV... syllables. Phonologically speaking, I don't know of any reason in Mandarin or Korean to treat initial glides as elements of a diphthong (I have no opinion of Cantonese). Although I would not be shocked to learn of a language with a contrast [wu] vs [uu], the obvious question to ask is why one is claiming that there is a diphthong [uu] as opposed to a long vowel [u:] (that is an answerable question, but it's a question that has to be raised).
Same-element diphthongs with the "glide" portion on the right are usually alternatively treatable as long vowels. This brings us to the question of where diphthongs come from in the first place: most often they come from long vowels, so /u:/ → uʊ → uo, uɨ.... I would say that [uu] and [ii] are the absolutely least likely diphthongs, because there would be no phonetic fact and hardly any phonological fact that could support such an analysis over a treatment of the nucleus as having a long vowel [u:, i:].
I try not to make predictions about the future of languages that I know nothing about. However, since you ask, I predict that [uy] is most vulnerable and would change to [ui].