And this create a practical/political problem that people speak a different dialect cannot recognize what this encoding is trying to express. Even though literally they share the same writing system.
I mean, yeah. You give up one thing and gain another. For instance, it would be much easier for people speaking those other "dialects" to learn to speak and understand putonghua, if they were seeing a phoenetic form of putonghua all around, rather than seeing characters which they read in their own words.
Alternately, we could all replace our spoken languages with Chinese characters. Then we could all read Chinese subtitles, and reach each others' languages to some extent.
But I think you'd be hard pressed to find anyone not already using Chinese characters for their own language who would consider the benefits worth the cost. It seems to me (as an outsider who's been studying the language for a few years) a sort of linguistic "Stockholm syndrome".
The case GP is talking about is (say) having subtitles in Chinese characters (in Mandarin), which can be read by people who speak Hokkien or Cantonese; or having street signs in Hong Kong written in "Written Cantonese", which can be read by people from Beijing.
The answer to the question, "How does someone from Beijing understand someone speaking Cantonese?" is generally, "They don't."
I think GP‘s point is that right now they can read the same text even if they can’t understand it spoken. Moving to a phonetic script would mean they can no longer read the same text, ergo worse
A phonetic/phonemic script would be worse for mutual intelligibility for those privileged enough to know written Chinese, which is notoriously difficult to learn.
But it might be better for literacy in general because it would be much easier to learn. And, though it is a comparably much more trivial issue, better for creating something like a morse code.
That said, I know there are many other issues apart from simple ease of learning that figure in to what language people learn or want to use. Written Chinese has a rich history and culture, and it's tied to people's identity so of course jettisoning it for something arguably more practical with the added downside of loss of mutual intelligibility among those who know written Chinese would likely result in strong opposition.
If you see the counter-arguments are coming from historical and cultural stuff, then you are making wrong assumption here. At least not in this branch. Literally you are the first one to mention this argument.
Think of Chinese as one script but multiple languages. The spoken languages have about as much diversity as European languages, but they all share a mapping to characters which are meaning based, not pronunciation based.
So you can use Mandarin pinyin, (though there are a lot of homophones) to serialize to a pronunciation, it wouldn't be understandable by a Cantonese speaker.
"Language" vs "Dialect" is a matter of degree. If you have a tiny bit of exposure to, say, German or Icelandic, you can actually catch a fair amount of what's said in those languages given the context. The same is true for Mandarin and Cantonese. A lot of the words really are just different pronunciations of the same word; 我 (me) is wo3 in Mandarin, and ngo5 in Cantonese; 你 (you) is ni3 in Mandarin and nei2 in Cantonese. A lot of the grammar concepts are the same; you don't conjugate verbs, you instead have "markers" that indicate things like "completed action" or "experienced action"; measure words, and so on.
But a lot of the grammar and words are just different -- at least in the spoken language; and typically subtitles are all in Mandarin.
So my son watches Peppa Pig in Cantonese; I can read most of the subtitles in Mandarin. Peppa will say, "Da4 di, nei2 tai2 ha2!" (Look, Daddy!); but the subtitles will say 爸爸,你看一下! (ba1 ba! ni3 kan4 yi2 xia4!) Note that only one of those four words is the same (你/ni3/nei2). "da di" (Cantonese) has been replaced with "baba" (Mandarin); "tai2" is replaced with "kan4" (a different character); and "ha2" has been replaced with "yi2 xia4" (an extra word).
"It's all Chinese" is a sort of fiction; and from my outsider's perspective, a fiction which heavily favors Beijing and the Han majority at the expense of the various minority groups. Written Mandarin is pretty close to spoken Mandarin; "official" written Cantonese is very different than spoken Cantonese -- to the extent that the verb "to be" is a completely separate word.