TA"Z on the Half-Hallel on the 7th day of Pesach
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The TA"Z in Shulchan Aruch uses the reason that the Egyptians fell in order not to say the entire Hallel on Shvii shel Pesach.
Right, but if you see the source in the midrash (Psikta DeRav Kahana) it's clear that it's the reason to recite the entire Hallel only one day and not to elude it completely. Otherwise it would be blasphematory to show ingratitude towards God's redemption. From the Yerushalmi it appears that the Hallel of the Seder night is because of the fall of the Egyptians in the Red Sea.