You can mix Japanese and Chinese with modern document authoring standards or with HTML, but the fact is that most people are too lazy to do that. It's a pet peeve of mine when a document gets displayed with a Japanese font but then falls back to another Chinese font when it encounters characters that are missing in the Japanese font. Even when the fonts look the same (or when you're using a unified CJK font like Noto), things will still look bad if the language is not specified, since some characters are written different in each language (or even different variants of Chinese), but still got unified[1].
I laud what TRON tried to do, but I don't think they had it right. They made the encoding too complex (especially for the 1990s) while Unicode offered a single Basic Multilingual Plane. Unicode quickly got complex too (mostly due to the mistake of adopting UCS2 and then repurposing that as UTF16 and adding surrogates, and later getting a little bit over the top with combining emojis),
but TRON was complex in other ways. If you mixed both Chinese and Japanese in a single documents, you had a multiple encodings to care about and control characters to switch between them. Suddenly, the character encoding is not stateless anymore. You can say the same about Unicode, but the statefulness of UTF-8 or UTF-16 is local and easily recoverable. Same goes for the statefulness combining diacritics, and bidirectional markers (which are rarely used) only affect the display. TRON code plane switches, as far as I understand, mean that even a simple text search or regex search would stop working and need to be completely redesigned, since it now has to be aware of which language we're reading right now! That's a big break, as you say.
> It also had a lot more characters. Unicode dropped some of the older or rare characters, meaning some people can't write their last name with the correct character on a computer with Unicode.
Only if they're very old and born before or during the war or its not their legal name. The Japanese government restricts the Kanji that can be used in names to Jōyō kanji (regular use kanji) and Jinmeiyō kanji (personal name kanji). Together they add up to roughly 3000 kanji. The list was back in 1991 when Unicode 1.0 was released, but it did include all of them, and many more, as did previous Japanese standards that predated TRON like JIS X 0208. I feel like the "people can't write their name" was always a bit of cope. Japan is still the country of "the nail that sticks out gets hammered". If your name falls outside of the legally allowed list of Kanji, you'll suffer even if you're running BTRON.
[1] https://en.wikipedia.org/wiki/Han_unification#Examples_of_la...