I can't really speak to the utility of using the characters in practice, but looking back on when I was studying Japanese and Korean, it frustrates me that more emphasis wasn't put on the characters, as learning the roots of the words was incredibly helpful in learning vocabulary, in the same way that learning Latin roots would be helpful in studying English. It was, though, much more of an issue in Japanese, where you run into the characters everywhere. Because of the heavy conversational emphasis in most foreign language classes, I didn't learn about character composition (radicals), or the phonetic element to characters until I took a bit of Chinese. When I did finally learn these things, my reading comprehension got a very significant boost.

I'd maybe argue that the use of Chinese characters in Japanese allows me to read much faster than if all writing were in Hiragana, particularly since people tend to identify words more by their shape, but Hangul does this quite well on its own, so I think maybe there's not as strong of a need for it in Korean.