Why is there no bracha of shehecheyanu recited when performing bedikat chametz, unlike other seasonal mitzvot (e.g. shofar, lulav, Chanukah lights, megillah)?
Taame Haminhagim (487–489) cites a few reasons:
- (from the Tur 432) because the search is for the holiday so the holiday's benediction covers it
- (from Avudraham) because we say that benediction only on something that brings joy and physical pleasure, whereas the destruction of one's food brings anguish
- (from P'ri M'gadim [MZ] 472:end of 2) because you're destroying something
msh210's excellent answer led me to two other reasons:
Ba'al HaIttur (quoted in Tur 432) presents an opinion that shehecheyanu is not recited because bedikat chametz is not strictly seasonal. If one leaves home many months before Pesach and intends to return to his house during Pesach, he must carry out bedikat chametz before he leaves. Thus bedikat chametz is not necessarily tied to a specific date.
Meiri on Pesachim 7a writes:
ונראה לי שמצוה שאין עיקרה לעצמה אלא להרחקת עבירה כגון בדיקת חמץ שהיא ליזהר ממציאת חמץ אין בה זמן
It seems to me that a mitzva whose purpose is not for itself, but rather to make a transgression less likely - such as bedikat chametz which is for [the purpose of] being careful to avoid finding chametz [on Pesach] - has no shehecheyanu.
[This answer of the Meiri is very similar to that suggested by DanF in his comments to the OP.]