I think that sɪ.ŋɪŋ does not seem too unreasonable as a syllabification of the word singing, so I'm a bit puzzled why that option for the syllabification of intervocalic /ŋ/ seems to be dismissed in all of the literature about English syllabification that I have encountered so far. To me, the analogy with sitting sɪ.tɪŋ or driving draɪ.vɪŋ seems fairly compelling: I don't feel like the identity of the middle consonant affects how I divide the two syllables of words like this. An alternative position that seems reasonable to me is ambisyllabicity, or Wellsian syllabification based on morphology and coda capture by stressed syllables. (Or more abstractly, there are analyses where [ŋ] in words like sing(ing) is treated as derived from underlying /ng/, but right now I'm not asking about those.) But many analyses of English syllabification that I have seen do not accept ambisyllabicity or coda capture, but instead use the Maximal Onset Principle to derive syllabifications like sɪ.tɪŋ or draɪ.vɪŋ. I don't see why ng in words like singing should be an exception to the MOP.*
It's true that /ŋ/ does not occur word-initially, or after other consonants. But the phoneme /ʒ/ is also marginal in word-initial position, and I think that advocates of the syllabifications sitting sɪ.tɪŋ and driving draɪ.vɪŋ would accept the existence of onset /ʒ/ in intervocalic position in words like invasion ɪnˈveɪ.ʒən.
Also, I can think of a number of examples from languages other than English that seem to support the idea that restrictions on word-initial consonants may be stricter than restrictions on syllable-initial consonants in intervocalic position. In native vocabulary, German lacks word-initial /s/ and /x~ç/, Korean /l~ɾ/, Hebrew /f/, French /ɲ/. But my understanding is that in intervocalic position, these consonants occur and are analyzed as onsets rather than as codas in these languages. (Well, I've seen a proposal to analyze German intervocalic [s] as a "virtual geminate" that in some way occupies both a coda and onset position, but that seems a similar level of abstraction to analyzing [ŋ] as /ng/, so I'd set it aside for the purposes of this question.)
Admittedly, some of the "restrictions" I mentioned in the previous paragraph seem to be fairly violable: e.g., in German, word-initial [ç] seems to be well established in a few non-native words, and word-initial /s/ in some loans from English; in Korean, /l~ɾ/ seems to be possible word-initially in loans; and likewise in Hebrew, word-initial /f/ seems to occur in loans.
But I'm not sure that the English restriction against word-initial /ŋ/ is actually much stronger: it seems to me that instead, there just isn't a lot of opportunity for English speakers to have pressure to produce word-initial /ŋ/ in loanwords. The sound has no unambiguous spelling in English, and it doesn't occur at the start of words from the languages that English speakers are most likely to have heard spoken aloud.
Has my argument here been made before by anyone else? Have I missed some strong argument against /ŋ/ being an onset rather than a coda in intervocalic position?
*I don't find the Maximal Onset Principle completely compelling as a major principle of English syllabification, but it seems that many linguists do. A modified principle of avoiding empty onsets specifically seems a bit more plausible to me.