Answer: The Gemara (Pesachim 120a) teaches that there isn’t the same requirement to eat matza on the last day of Pesach as there is on the first night. The Shulchan Aruch Harav (OC 475:32) explains that when the Torah tells us to eat matza on the other days, it clearly means to eat something other than regular bread.
There is a machlokes among the rishonim and acharonim¸ however, as to whether one performs a mitzva by eating matza on the remaining days of Pesach. According to Ibn Ezra (Shemos 12:15), one is obligated to eat matza all seven days (See Chizkuni 12:18).
R’ Ovadia Yosef (Yechave Daas 1:22) quotes the Baal Hamaor (Pesachim 26b) who asks why we don’t recite a beracha when eating matza throughout Pesach, just like we do upon eating in a sukka following the first day of sukkos. He answers by differentiating between Pesach and Sukkos, when one can live for six days by eating other food, thus one has a choice to eat matza or not. One cannot live for six days on Sukkos without any sleep. As one has no choice, therefore, but to live in a sukka, they recite a beracha upon performing this mitzva. According to R' Avraham Borenstein (Avnei Nezer OC 377), the Baal Hamaor holds that eating matza after the first day to be an optional, rather than an obligatory mitzva.
Similarly, the Vilna Gaon (Maaseh Rav 185; Kesav Vehakabala, Devarim 16:8; Mishna Berura 475:45; 639:24) maintained that while one may not be obligated to eat matza throughout Pesach, one still fulfils a mitzva by doing so. Thus, he would make a point of eating seuda shelishis on the last day of Pesach even though he wouldn’t normally eat seuda shelishis on Yom Tov (See Aruch Hashulchan OC 475:18).
Sefer Hamichtam (Sukka 27a), the Meiri (Pesachim 91b) and the Orchos Chaim (Sukka 36), however, maintain that there is no mitzva to eat matza following the first night. Likewise, the Magen Avraham (639:17) quotes the Maharil who writes that we don’t say a beracha as there is no obligation.
R’ Ovadia Yosef writes that even according to the Vilna Gaon, saying a beracha upon eating matza other than during the seder would be a beracha levatala (beracha in vain).
R’ Eliezer Waldenberg (Tzitz Eliezer 10:27:5; 13:65) writes strongly against those who have the practice to avoid eating matza out of concerns for their kashrus, stressing the importance of washing for pas over Shabbos and Yom Tov.
In conclusion, while we only say a beracha upon eating matza during the seder, some rishonim and acharonim maintain that one fulfils a mitzva by eating throughout Pesach.