While there is a “floor” to the complexity of a script in its ability to faithfully reproduce a langage, there is no “ceiling”, you can always pile on complexity.
Although I would say that logographic scripts are the other kind of complexity, they’re complicated to learn and use because they’re simplistic in their approach.
Syllabic or alphabetic scripts require higher concepts, but that makes them more flexible and composable.
Hangul is simpler, that’s not really in dispute. It was literally designed to be simple so that a native speaker could become literate in ten days.
Hangul is not phonetic, it's a morphophonemic script. The Korean language has a lot of rules that applies at different boundaries, which make the pronunciation of words different from what is written. The best example of this is the "Korean wave" /han/ + /lyu/ => [hallyu], written has "hanlyu" (한류) which is conforming to the phonemic decomposition but certainly not to how the word is pronounced.