It's interesting from a linguistic point of view as a false-beginner retaking my second language in my intermediate-ish third language. It does seem like the Hangul script is not really up to the task of representing Chinese sounds without some large and major changes.
On the contrary, the hangul script itself has tons of obsolete jamo (letters), some of which date from King Sejong's time, whilst Korean had some form of indication for pitch in the form of dots. So it's somewhat possible to potentially indicate tones or other sounds of Chinese.