> Actually, the alphabet invention was precisely that the same alphabet could be used for different languages.

No. Multiple languages were written with the same alphabet because of the borrowing of that technology by speakers of other languages, not because it was designed as such.

Actually the process of borrowing is fondamental to the emergence of alphabets: the three biggest (by corpus size) logographic scripts all gave birth to more phonetic scripts across language boundaries. That happened with hieroglyphics (the case we are discussing), but also with Sumerian cuneiform > Akkadian writing and Chinese characters > Japanese kanas.