Why do we recite Al HaNissim in birchas hamazon but do not insert any mention of Chanukah in Al HaMichya, even though we mention other significant days like Shabbos and Rosh Chodesh? Rav Shternbruch suggests that the chiyuv to mention Al HaNissim stems from the chiyuv to give hoda'ah on the nes; therefore, it belongs in Birchas HaMazon where we have Nodeh lecha..., a specific bracha of hoda'ah. Al HaMichya is an abbreviation of bentching and has no specific bracha of hoda'ah; therefore, hoda'ah on the nes does not fit.
I think this approach may depend on how you learn the sugya in Shabbos 24a. The gemara raises the question of whether Al HaNissim must be recited in birchas hamazon or not. Why did the gemara take as a given that Al HaNissim must be recited in tefilah, in shmoneh esrei, but have a doubt about whether it belongs in bentching? Rashi explains that takanah to celebrate Chanukah with "hallel v'hoda'ah" by definition implies commemoration of hoda'ah in tefilah. (I think what Rashi means is that mentioning the nes of chanukah is clearly apropos in tefilah, where we give thanks for "al nisecha she'b'chol yom imanu." It is less clear that this type of hoda'ah for nes fits the theme of bentching.) Tosfos, however, explains that reciting Al HaNissim in tefilah was a given because tefilah is done b'tzibur and therefore there is a kiyum of pirsumei nisa. One can learn the gemara's conclusion on one of two ways: either pirsumei nisa applies even in meals, or perhaps the fact that we recite Al haNissim in bentching is evidence that the entire premis that the obligation Al HaNissim stems from pirsumei nisa is wrong.
It sounds to me like R" Shternbruch's chiddush fits better with Rashi's view. According to Tosfos, Al HaNissim is potentially a din in pirsumei nisa and is as much an intrusion into bentching as it would be in Al HaMichya.
Rav Soloveitchik (Igros haGRI"D, Hil Brachos) has an ingenious answers to this question of why Al HaNissim gets no mention in al hamichya. He suggests that the chiyuv of mentioning Ya'aleh V'yavo or Retzei, the obligation to mention mei'ein ha'meora, is an additional kiyum tacked on to the mitzvah of Birchas Ha'Mazon. Al HaNissim, however, is not an additional kiyum, but is part of the nusach habracha of birchas hoda'ah of Birchas HaMazon. In other words, Chazal dictated that a different nusach habracha be said for Nodeh lech... on Chanukah. Saying Al HaMichya instead of full bentching does not suspend the need to fulfill the additional chiyuv of mentioning me'ein ha'meora. However, given that Al HaMichya is a shortened form of bentching, just like other parts of Nodeh lecha... are cut out, Al HaNissim can be cut out as well.
(There is supposedly an answer to this same question given by the Brisker Rav -- if someone knows where it is and can explain it, please let me know).