That's only really true when the entire string is using CJK characters, but as far as I know, that's going to be fairly rare.

For example, this Chinese Wikipedia page is almost twice as big in UTF-16 as in UTF-8, because the vast majority of the content seems to be HTML tags:

  $ curl -s 'https://zh.wikipedia.org/wiki/中华人民共和国' | wc -c
  1877366
  $ curl -s 'https://zh.wikipedia.org/wiki/中华人民共和国' | iconv -f utf-8 -t utf-16 | wc -c
  3345724

If I strip out all the printable ASCII characters, it does indeed become about 33% more compact in UTF-16:

  $ curl -s 'https://zh.wikipedia.org/wiki/中华人民共和国' | tr -d '[:print:]' | wc -c
  311226
  $ curl -s 'https://zh.wikipedia.org/wiki/中华人民共和国' | tr -d '[:print:]' | iconv -f utf-8 -t utf-16 | wc -c
  213444

With gzip compression it is only about 10% more compact:

  $ curl -s 'https://zh.wikipedia.org/wiki/中华人民共和国' | tr -d '[:print:]' | gzip -9c | wc -c
  98373
  $ curl -s 'https://zh.wikipedia.org/wiki/中华人民共和国' | tr -d '[:print:]' | iconv -f utf-8 -t utf-16 | gzip -9c | wc -c
  89031

So I guess if you're archiving pure CJK text, maybe you could get a 10% benefit, though I suspect non-Unicode encodings of that text would be more compact anyway.