tefilla - Why is 'misod chachomim unevonim' sometimes said and sometimes omitted in the repetition of the Amidah?

In Askenazi communities, the piece beginning 'misod chachomim unevonim' is said at the repetition of the Amidah at Shacharis when there are piyuttim (except Purim) and on Musaf on Yomim Noraim as well as, in my Machzor, at Mincha and Neilah on Yom Kippur.

I thought the reason was to establish permission to “interrupt” the Amidah with these additional prayers.

But it is not said before the piyuttim in Musaf on (1) Shabbos Shekolim and (2) Shabbos Ha'Chodesh and at the beginning of the (3) Krovets on Purim morning.

Why not?