I have a Taiwanese book for school children that includes the governments romanisation, hanzi, and some kind of extended bopomofo. While the native speaker I was learning with could read hokkien-with-characters, he couldn't do it quickly, and often had to puzzle over a certain character. In cases where they had both characters and romanisation I was able to help him on the characters he was stuck on by (badly) pronouncing the romanisation. Still, I haven't met any Taiwanese hokkien speakers at all interested in romanisation. Which is a shame - it covers all the sounds, and the language does seem to be slowly dying (the fact people don't write it probably has a lot to do with it).
Though it seems like hokkien-with-characters is a thing (from what you say, and also from what I've seen with 4-bopomofo ruby and Wiktionary), just less prevalent. Or perhaps one can look at hanzi at the same level as romanization for Hokkien (except romanization is more prevalent), i.e. "someone else's script that kinda works for us so we use it sometimes"
I'm surprised the extended bopomofo (I assume it's https://en.m.wikipedia.org/wiki/Taiwanese_Phonetic_Symbols which actually till now was the thing I thought was bopomofo) is used more as a writing system for Taiwanese.
But I'm actually unclear about this.
The weird thing is that certain dictionaries give pronunciations of hanzi in multiple Chinese languages (e.g. Wiktionary) including "scriptless" languages.
I've also seen cases in Taiwan where e.g. a restaurant name or place name is written in hanzi and English and the romanization is clearly not using the standard Mandarin pronunciation of the term. An example of this is 淡水 which is romanized "tamsui" in Taiwan but would be "danshui" in pinyin or "tanshui" in Wade-Giles. Syllables ending with "m" are not a thing in Mandarin as far as I know, and 水 is never romanized as "sui" (though I could chalk the 水 one up to an alternate local romanization system like POJ, which I don't know anything about).
Finally, I've also seen text in Taiwan with four-bopomofo ruby. From my understanding of bopomofo; for Mandarin you won't have more than three glyphs plus a tone mark -- the initial consonant, optional medial i/u, and optional final. This also gives me the impression that Min Nan can be written in hanzi. Unless Taiwanese Mandarin differs from Mandarin significantly in pronunciation (which may be the case, I don't know).
All this leads me to believe that other Chinese languages can use hanzi, but do so less often, perhaps? This is something I've always been confused about but never really looked into it.