You're making the same mistake: the languages are different, but the script is the same (or trivially derived from the Han script). The Ideographic Research Group was well aware of this, having consisted of native speakers of the languages in question.

That's not "mistake", that's the reality. They don't exchange, and they're not the same. "Same or trivially derived" is just a completely false statement that solely exist to justify Han Unification, or maybe something that made sense in the 80s, it doesn't make literal sense.