Take your example of 仲. How is that pronounced? In Japanese, 人 is typically pronounced "jin", "nin", or "hito" depending on context. 中 is usually pronounced "chuu" or "naka." How do I know these things? Rote memorization. While I can recognize that 仲 contains 人 and 中, that doesn't tell me how to say 仲. The only reason I know its pronunciation is because I memorized it. (In this case, it happens to be the same as 中.)
And that's just for reading. Writing is worse. Character amnesia is extremely common among native speakers of Chinese and Japanese. From Wikipedia[1]:
> Another anecdotal example can be seen during a spelling bee show hosted on CCTV in 2013, where only 30% of participants were able to write "toad" (Chinese: 癞蛤蟆; pinyin: Lài há ma) in Chinese.
That sort of thing simply can't happen in phonetic writing systems.
You are correct, though: This is not failsafe and characters can have multiple readings or lack this phono-semantic notion altogether (also, since the characters are originally Chinese it doesn't work as well in Japanese, I believe), but I think it is the closest thing to guessing a word's pronunciation that these languages offer.
[1] https://en.wikipedia.org/wiki/Chinese_character_classificati...