A big reason is of course the possibility of using arbitrarily complex letters or symbols, thus allowing Kanji (and Hanzi) to be used.
I'm reading a book right now on the difficulty that Hanzi brought to the developing china of the early 20th century [1]. The difficulties are all mostly predictable - cultural attachment, the fragmentation of languages and dialects, transliteration of tonal variants, finding a large enough keyboard etc.
But there are some interesting things I didn't know, for example that there were attempts to decompose symbols into radicals that could be combined.
Crests, coats of arms, flags... these things kinda-sorta died out in America. (Indeed: people came to America to escape the Nobility's culture from Europe). But Japan has a lot of families with "samurai" lineage, the old Nobles from 500 years ago... as well as a connection to their families crests, emblems, flags, etc. etc.
Culturally, its important to at least enough of them, to keep those traditions alive. Fax works for that. Email doesn't seem to quite do the family seal/mon justice.
After all, if you've got this stamp that's been in the family for the past 300 years, you're gonna want to keep using it for tradition's sake. (Maybe not the actual 300-year-old family relic, but replications of it on modern rubber).
You might actually be thinking of hankos, which are widely used in every-day paperwork, and they are usually a personal seal rather than a family seal. I don't think they're high culture, as almost everyone has one and they're used for day-to-day document signing of many types of documents, like opening a bank account or filing taxes and so on.
They're also part of some important business practices. One such practice called nemawashi, which is a "peer consensus" required for big decisions in some companies. A document outlining the change or project you want to undertake circulates to all peers or superiors it would reasonably affect, and they must all sign with their hanko in order for the process to be accepted.
Although there are some high-culture elements to them, such as having a bigger hanko if you're in a higher position in the company, some etiquette around hanko placement on the page depending on your rank in the company. There is also a tradition of giving a fancier hanko as a coming of age gift, those used to be of ivory (and still can be, Ivory in Japan is a fairly fascinating topic in itself).
You mean e-signatures? Which is what I use in my office whenever we sign documents around here?
I'm sure Japan knows about e-signatures. The problem is that of "culture" perhaps? I'm not entirely convinced that this stamp-thing is a bad thing for Japanese culture, or that this is an issue that needs "fixing".
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But "if it does need fixing" (and again, I don't think I agree with that mindset...), e-signatures are readily available and easily done in Adobe-PDF readers, backed up by public/private key infrastructure given out by your company's smartcard system (or whatever).
A number of government regulations still require hankos, which is one of the reasons e-signatures aren't more heavily used. The government has been aiming for digitalization, and part of that is eliminating regulations that require hankos, so e-signatures have been becoming more usable lately.
Hanko culture, however, is harder to kill off. Part of that is things like more senior employees having larger hankos, needing to tilt your hanko signature to "bow" to your managers, etc. Japanese E-signature platforms generally have seals, and offer features to change the size of the seal, and to rotate it, to support the cultural aspects of hanko culture.
Surely everyone can type Kanji now though? I could see that being an issue adopting to typewriters from handwriting, but now I assume those issues have been fixed. There's not many symbols you can't represent in Unicode and people aren't making up new symbols commonly.
Like, these faxes are still typed and printed first, right? People aren't just handwriting everything. About the only advantage of faxes in such a situation is the ability to personally sign/stamp something easier.
I used to work for a company doing Japanese handwriting recognition, and we would sometimes get request "can you support kanjis not in unicode" and "lost" contracts because we could not. This is especially the case for rare Kanji for family names, etc. I still have no idea how those customers actually handle those kanjis in their systems, must be fun.
Ummm.... China/Japan was making up new symbols constantly. Which is why UTF-16 failed. We Westerners have small alphabets and less of the image/iconography culture than the Eastern world.
I can absolutely see this "iconography" culture in China/Japan being a major reason for fax machines.
To be pedantic, what failed was UCS-2, the enconding formerly known as just 'Unicode'. UTF-16 was introduced with version 2.0 of the standard and can encode all codepoints thanks to the surrogate pair mechanism.
I'd expect print to standardize on a subset originating in the days of physical type and manual setting, when every character removed from the printing set would ameliorate very real costs at just about every stage of production.
In my younger days I started a project to create Han characters from radicals in Metafont. It was an ambitious project which, sadly, was beyond my skills. A smaller-scale idea, assembling Hangul from individual letters was more feasible, but the realities of school and work were enough to keep any of this from getting beyond initial demonstration coding. In a parallel universe, this was my senior project in undergrad and was finished in 1990. Some of my parallel universes are really amazing places.
I'm reading a book right now on the difficulty that Hanzi brought to the developing china of the early 20th century [1]. The difficulties are all mostly predictable - cultural attachment, the fragmentation of languages and dialects, transliteration of tonal variants, finding a large enough keyboard etc.
But there are some interesting things I didn't know, for example that there were attempts to decompose symbols into radicals that could be combined.
[1] Jing Tsu: Kingdom of Characters.