This is a question specific to Ashkenazim (Nusach Ashkenaz, Nusach Ari, and Nusach Sefard).
On Shabbat, after the Torah Reading and before Mussaf, 3 prayers, (2 Yikkum Purkans and a Mi Sheberach) are recited. On Yom Tov that falls out on a weekday, we are instructed to skip those prayers.
Why skip Yikum Purkan and the Mi Sheberach for the congregation on a holiday that falls out on a weekday?
There doesn't appear to be any Shabbat specific text, so why omit it?