The Beis Yosef (O.C. 432) in fact quotes the Ba'al ha'Itur as saying that there is an opinion to say Shehecheyanu. The Teshuvos ha'Rashba (1:223) also quotes this opinion, but says that we do not say Shehecheyanu because it is a Mitzva that does not really have a set time, as one who is leaving town and plans to come back right before Pesach must do Bedikas Chametz even in the beginning of the year. The Aruch Hashulchan (O.C. 432:4) says that there is no Shehecheyanu because it is not a Mitzva that is one of Simcha. Alternatively, the Aruch Hashulchan says that one is Yotzei his Shehecheyanu with the Shehecheyanu of Pesach night (see Be'air Heiteiv O.C. 432:1).

All the best,

Yaakov Montrose

The Berachah of Shehecheyanu is a Berachah that Chazal instituted to make on either an intrinsically joyous occasion which comes at a certain time during the year, or during certain unique events which someone experiences with great happiness. The Shehecheyanu on Mitzvos is of the first nature, while the Shehecheyanu on new clothes is of the second. The Berachah of Shehecheyanu is only said on Mitzvos that are rare, even if a person does not feel happy when, for example, making Kiddush on the first night of Yom Tov (although he should). On the other hand, the Berachah of Shehecheyanu on new clothes is largely dependent on the person's personal Simchah when making a purchase. It therefore is not relegated to having to be at a certain time, as the Gemara states that when hears joyous news, he makes either a Shehecheyanu or Hatov v'Hameitiv. The Shehecheyanu on new fruits, in fact, is only made on fruits which are seasonal, not on fruits that are accessible year round (like Mitzvos. See another similarity between Shehecheyanu of fruits to Mitzvos, and not clothes, in v'Zos ha'Berachah by Rav Alex Mandelbaum p. 166).

Kol Tuv,

Yaakov Montrose