When Al Hamichyah is recited on a holiday or on the sabbath, it has a short passage inserted relevant to the day. However, there's no addition to Al Hamichyah for when it's recited on Chanukah: Chanukah is not mentioned at all in the blessing. Why not?
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The Minchas Ani says that Al Hanisim when said in Birkas Hamazon, is considered an insert. It is not a special Beracha in the Birkas Hamazon. But, if we would add an insert in the Al Hamichya, people might come to think that Al Hanisim deserves its own Beracha.
See this link from Rabbi Eli Mansour for more detailed answer