In general, we have absolutely no problem with CJK in Postgres. Search is very application specific and some of our users want to do things like kana + kanji search. [1] I don't even know where you would start with that in Postgres.
We also need stuff like language detection and analysis of mixed language data.
A big advantage of going with a dedicated search tool is that it teaches you what you don't know about search, and it turned out that we knew pretty much nothing.
[1] https://www.elastic.co/blog/implementing-japanese-autocomple...