Chinese: the physical layout is always ANSI US. Depending on the IME you might want more than roman characters printed on keycaps, but it's just cosmetic if you can touch-type.
Japanese: most keyboards use the JIS layout and visually support multiple IME, but if you stick to romaji, using an ANSI US keyboard works too.
Korean: the physical layout is ANSI US (sometimes with 2 extra modifiers). Hangul is a proper alphabet, symbols are made up of subcomponents (jamo) that are printed on the keys. Again it's just cosmetic.
In my experience, people of my generation (30-40 years old) who are educated know to touch-type. For instance I've never met a Taiwanese that needed to look at the Zhuyin symbols on a keyboard.
But I've heard that's not the case anymore with kids that grew up using smartphones.
What I like about using US Intl (I've modified it slightly) is that no switching is required, I can conveniently enter both the programming related characters (such as curly braces which require gymnastics with a German keyboard layout) and the German specific characters such as umlauts.
But I can't imagine that this could be possible for Chinese without switching modes (or input methods or keyboar layouts).
You can write the characters using digraphs.
For example, type <"> and then <a> to get <ä>. Type <"> and then <space> to get <">.
This won't work for other alphabets, of course.
Not sure what CJKV users do.