But usually people only care about their language, so it goes by the system UI language and it works out.
Sure. And once you're doing that you don't gain a lot of benefit from unicode AFAICS, because you have to track these spans of locale-specific text.
UTF-8 already has different codepoints for every other language, like I can type russian (День), greek (Ημέρα), english, even egyption hieroglyphs (𓀃) all of them in this one text field, and they all render right for both of us if we have a suitable font. If they don't render, it's unambiguous.
It's only chinese and japanese where I can type some characters, and depending on if you have a chinese or japanese font _first_ in your system, it might render wrong, and either way it's ambiguous to the computer without further metadata. The computer doesn't need metadata to know that "α" is "α", why does it need metadata to know if 直 is the chinese (http://www.hanzi5.com/bishun/76f4.html) or japanese (https://kanjivg.tagaini.net/viewer.html?kanji=%E7%9B%B4) character, two different looking characters that share the same codepoint.
Because Unicode is about the meaning of characters, not their appearance. If there were a context where the two different shapes of 直 have different meaning, Unicode would add a new codepoint to distinguish them. In fact "ɑ" without hook does have a separate codepoint because it is used in linguistics to mark a vowel different from "a".