Yaaleh veYavo is said on occasions where Hashem helps us in ways that go beyond the natural order. Therefore, wouldn’t it make sense for it to be composed with eight terms of ascent, going beyond the world created in seven days? What would be the motivation for folding “veyipaqeid veyizakheir” into one, and reducing the count to seven?

Yishar Koach.

Tzadok HaCohen of Lublin ztz”l writes in Poked Akarim that Hashem’s remembrance of Sarah was the first instance of such a thing happening since the Creation. That is the significance of פ-ק-ד; it’s an initialization. Prior to this, an akarah, a barren woman, was an akarah forever. Once Yitzhak was conceived, it no longer required a miraculous change in Nature for an akarah to conceive; similarly for the various miracles that happened for our ancestors. If I recall correctly, he implies that now, for us to receive the same miracle (only!) requires ז-כ-ר –a recollection of a process that has already been initialized.
This understanding of פ-ק-ד vs ז-כ-ר seems to fit with the idea from Rav Dessler that our individual tafkid is unique. And it would also imply that for us to merit Hashem’s remembrance, we need to desire to fulfill our individual tafkid with the same intensity that Sarah desired a child.

May it be so for all of us.

Ksiva ve’chasima tova