One of the reasons was that it was simply easier to standardise Chinese input. It's not just Kanji (here i'm referring to all 漢字, not just Japanese characters) that's the issue, but also encoding of kana. Chinese in the PRC could easily settle on GB (国标 guóbiāo) encoding, and Taiwan on Big5. A single standard was applicable in both places.

In Japan, there wasn't an easily dominant single standard. Multiple standards proliferated, some becoming dominant in only certain areas of life. In earlier versions of Unicode when z-variations weren't well supported (and which, for what it's worth, are still really poorly handled on most client side applications of the standard), which prevented Unicode from easily eliminating the other character encoding systems.

Complicating matters is that things like computers and phones didn't have a unified standard either, so if you had one good solution for kana on one, that doesn't mean the same is going to happen on the other. Mobile phones were huge in Japan and in a lot of different ways than they were in other countries, and so the character encoding that gained prominence on that platform became deeply entrenched. As personal computers started to become more common (around when the AskHistorians 20 year rule comes into play, so I'll tread lightly here), encoding systems developed differently than they had one phones, and just based on inertia it was never likely that one system was going to simply replace what had become standard on the other.

Myanmar actually has this same situation, and there is nothing like kanji to deal with there. But thanks to early development with one encoding system (which is awful and called zawgyi ဇော်ဂျီ) becoming so entrenched that even though Unicode is the official standard encoding in Myanmar, even the government doesn't use it, because zawgyi is what most people have set up their devices to read. Now we're definitely breaking the 20 year rule, but I bring this up by way of analogy, and one about which there are plenty of more recent pieces that have been written in case you or anyone else is interested in the same sorts of problems Japan has had with encoding.

So back to Japanese, it's not that Kanji are difficult. They're fundamentally not, unless you're the guy having to make the typeface. The issue is that multiple systems were in use (kana, kanji, romaji) and no single solution handled all of them well, and no single solution gained a strong foothold in all electronic devices.

The hanko point is valid. In Taiwan this is also still the case; your personal seal is your signature for a lot of things. Buying a car? Seal. Opening a bank account? Seal.

There's also one thing China has done differently than the West, and that relates to this point from the article:

Even today, particularly for older Japanese people, it’s easier to write a letter by hand than with a standard keyboard. Japan also relies on seals, called “hanko,” that are required for most official documents.

In China, miniature handwriting recognition tablets (think tiny Wacom tablet) have always been big sellers. They are still converting the input into GB or Unicode, but for many older people, the situation is the same as in Japan; handwriting is easier. So then you could ask why these haven't fully replaced fax machines in Japan. But if you're handwriting already, you could then deal with the OS and try to compose an email, but if you've got a fax machine already (and you do because they're everywhere), then why not just fax something you put on paper.

I will make one more point that has more to do with the premise of the question. America hasn't fully moved past fax machines, or at least hadn't as of a few years back. A lot of things still required faxes as recently as 2010 when, to sign documents without being there in person, fax was suggested as often as scanning and emailing was. Maybe that's changed in the last 8 years, but I bring it up just to illustrate that some times old tech sticks around because it's still useful and change is hard. Just look at how little improvement has been made to computer printers in the last 20 years. That's not in answer to your question but rather just to the point that, while most people don't use faxes regularly in America, they're still around and in use. But so is Windows 3.

tl;dr:

• China mostly only had to standardise one system on one platform.

• Encoding in general has been a major issue on computers, even outside the CJK area.

• Faxes are still useful and used around the world.