It probably could have been resolved with superscript numbers and a strictly controlled dictionary that mapped each number to a specific dictionary definition for a homophone. But that's not what happened and instead we ended up with Simplified Chinese which is still among the most complex written languages ever created.
I believe it's still used in some dictionaries as a pronunciation guide however.
I can't speak for Chinese, but for Korean there's a large number of Chinese loan words, except spoken Korean doesn't have tones and it does introduce a number of comprehension issues when context is ambiguous and the different words are written with the same Hangul. This wasn't really an issue in the past as Korean used the Chinese system until Hangul started becoming more commonplace.
https://en.wikipedia.org/wiki/Bopomofo
http://www.omniglot.com/writing/zhuyin.htm
https://en.wikipedia.org/wiki/Simplified_Chinese_characters
http://hunjang.blogspot.com/2005/04/koreans-reading-comprehe...