The problem with that would be that every software must know the intricate rules about combining glyphs, and if they guess wrong, users get garbage characters.
Considering that the majority of code is written by people who don't know Chinese characters, it would result in never-ending issues, pretty much everywhere.
Korean actually has a two-way system in Unicode. Every conceivable character (= syllable) possible in modern Korean has its own codepoint, which allows most software to display them correctly: from their point of view, it's just another CJK character.
On the other hand, there is a Unicode area containing Korean sub-blocks ("jamo") that were used historically. In theory, you can combine them and get some pretty funky archaic syllables. Almost no software renders them right.
They can't even get much simpler things right. Qt incorrectly combines accents with the character to the right instead of the left and has been refusing to fix this bug for years.
Considering that the majority of code is written by people who don't know Chinese characters, it would result in never-ending issues, pretty much everywhere.
Korean actually has a two-way system in Unicode. Every conceivable character (= syllable) possible in modern Korean has its own codepoint, which allows most software to display them correctly: from their point of view, it's just another CJK character.
On the other hand, there is a Unicode area containing Korean sub-blocks ("jamo") that were used historically. In theory, you can combine them and get some pretty funky archaic syllables. Almost no software renders them right.