From here [0], 94.1% of .jp websites use UTF-8 and 6.5% use Shift-JIS. You can find a list of popular sites still using Shift-JIS here [1].
If you change your PC or your phone locale to Japanese and access mostly Japanese website, the font display on most major OS works well. It's probably fair to assume that's a very common setup for Japanese users, and probably for Chinese and Korean users as well.
I think the CJK "problem" is more apparent for international users who don't have the locale setup or dealing with multiple languages plain text at the same time.
[0] https://w3techs.com/technologies/segmentation/tld-jp-/charac...