Unicode, in some cases, did avoid separating characters out, and that was also a mistake that damaged existing alphabets irreparably.
See the Han unification [0] effort.
There are characters in Japanese and Chinese which are similar, but written differently in each... And they ended up using the same codepoint in unicode for them and relying on different fonts.
So now I can't easily quote a japanese sentence in a chinese book without having to use two different fonts, which seems quite silly.
Worse yet, there were many common glyphs in use (especially for names) that were unified out of existence. There are literally people who couldn't type their names in unicode. There are a lot of works of text that can't be faithfully OCRd due to not having certain character variants that were unified away.
Okay, so why wasn't the cyrillic alphabet unified with the latin one even if the japanese and chinese ones were? Clearly Han unification did much more damage than cyrillic unification would have.
Well, the answer is sorta politics. ISO 8859 is what came before Unicode, as far as the unicode consortium is concerned. Since ISO 8859 encoded latin and cyrillic separately, that got carried over for "compatibility". Because the unicode consortium and ISO 8859 were both more western-centric, and CJK users had already dealt with things in a way that was standardized only over there, not in any western ISO standard, of course the unicode consortium would honor the existing ISO standard and ignore the CJK standards.
[0]: https://en.wikipedia.org/wiki/Han_unification