Fancy punctuation is supposed to be about correctness of the codepoint, not about trying to transcribe graphics into text. Recent example - Edit #82550890 - MusicBrainz
Like you said, MIDLINE HORIZONTAL ELLIPSIS (⋯ U+22EF) is a math symbol. Thus, JIS X 0213 - Wikipedia does not include it, and uses HORIZONTAL ELLIPSIS (… U+2026) instead.
Similar to how we want to use Katakana-Hiragana double hyphen (゠ U+30A0) rather than fullwidth equals sign (＝ U+FF1D), because we’re writing Katakana/Hiragana, not Math.