For anyone who, like me, has been plagued by the constant need for a font that looks nice for Chinese, Japanese, and Latin scripts, I'd like to bring the M+ font to your attention. To quote the Arch Wiki's description of it:
"Modern Gothic style Japanese outline fonts. It includes all of Japanese Hiragana/Katakana, Basic Latin, Latin-1 Supplement, Latin Extended-A, IPA Extensions and most of Japanese Kanji, Greek, Cyrillic, Vietnamese with 7 weights (proportional) or 5 weights (monospace)."
To see its support of Chinese characters, I went to Ctext and glanced over a chapter from the Mengzi 孟子. Not a rigorous test, but a good indicator of the font's usability for Chinese too, I think. I am disappointed that it doesn't display the character 者 with the 丶 over the 日, but since that is only preserved in the Korean usage of Chinese characters, it's not surprising this font doesn't have that tiny detail.
I just found it and am very pleased with not only its character support, but also how those characters look. I think my struggle for a font that looks equally good across the various scripts I daily work with is over.