There seem to be two separate explanations as to why we only say a "half" hallel on the intermediate and final days of Pesach. According to one opinion (as attributed to the Shibolet Haleket here) it has to do with muting our joy at the fall of our national enemies.
But then why is the same logic not applied to the first day(s) of Pesach which followed the deaths of (relatively innocent) firstborns. I understand that one could say that this midrashic explanation is persuasive only when combined with the talmudic one, so when the gemara does not give a reason, the midrash cannot stand on its own, but according to footnote 5 on that Web page, the Taz seems to say that the midrash is enough on its own! If so, why wouldn't the Taz apply it to the first days?