A simple reasoning.
The pikuach nefesh is to eat, not to make the mitsva. So, eating need a bracha because it overrides the isur (by the way, see SA oc 204, in nos'e keilm, some poskim said that if he feels bad because of the fact that he eats prohibited food, there is no really hanaa and he cannot bless), the mitsva however, per se, cannot override the isur, because to lose a mitsva is not physically lethal. So, without the nutritional need, he will not make it (in the case of achilat matsa), so he is patur and cannot bless for the mitsva.
By the way, it's stated that one doesn't fulfill the mitsva eating tevel
Psachim 2.5
אבל לא בטבל, ולא במעשר ראשון שלא ניטלה תרומתו, ולא במעשר שני והקדש שלא נפדו. חלות תודה ורקיקי נזיר--עשאן לעצמו, אין יוצא בהן
So we have an answer from svara, the cause of the infraction is the need to eat, not the need to fulfill the mitsva, so the mitsva is not a duty, and the beracha is on the Tsivui, and this is demonstrated, in several mishnayot regarding birkat hamazon, eruvin, matsa and Maror, one of the cases is quoted as example.
In poskim.Rambam is one of the Rishonim who exempt from blessing on a prohibited food anyway.
Regarding the birkot hanehenin for prohibited foods in a situation that allows their consuming (Bet Yosef OC 196, 204),, there are several opinions in rishonim, Rambam, Raavad, Rosh, Rabenu Yerucham, Rashba, Rosh. The discussion addresses bracha rishona an acharona, (bhm and motsi). The reason of the opinions that one does bless is the hanaa. Regarding birkat hamitsva, despite that the mitsva is to be nehene (to eat), the hanaa is not the cause of the mitsva, but one the conditions, so no one of our poskim addressed a chyuv to bless bircat Hamitsvot. We need to check our assumption in BY OC 196, here is a quote around a passage of Yerushalmi.
גרסינן בירושלמי פ"ק דמסכת חלה תני מצה גזולה אסור לברך עליה א"ר אושעיא על שם ובוצע ברך נאץ ה' הדא דאמרה בתחלה אבל בסוף דמים הוא חייב לו רבי יוסי אומר אין עבירה מצוה א"ר אילא אלה המצות אם עשיתן כמצותן הרי הן מצות ואם לאו אינם מצות. ומשמע דלרבי יוסי ורבי אילא בסוף נמי אינו מברך על מצה גזולה. ואין לדחות ולומר דאדרבה משם ראיה דטעמא דמצת מצוה היא הא לאו הכי שפיר מברך עליה דהא איכא למימר דבה"מ נמי מצוה היא דכתיב ואכלת ושבעת וברכת והא דנקט מצה להודיעך כחו דר' אושעיא דאע"ג דאיכא נמי מצות מצה מברך בסוף. וההיא דהרי שגזל חטים וכו' נמי כדברי הרמב"ם דייקא לפום נוסחי דידן שכתוב בהם כיצד מברך אין זה מברך אלא מנאץ דמשמע דמתמה כיצד אפשר שיברך והלא אם היה מברך אינו אלא מנאץ הלכך לא יברך...
You can follow a reasoning regarding mitsvot - hanaa comparison, our topic. One of the sides argued that there is no proof from Yerushalmi that one cannot bless on prohibited food. Because the Yerushalmi, is discussing birkat "al achilat matsa". Birkot hanehenin are different and are related to hanaa. (This is our svara above!). The second size, that stands up for Rambam, and says that the Yerushalmi is a proof that one cannot bless on a piece of isur. In a first time, BY says that can interprete that the pshat of the first svara, is: One needs to bless regarding birkat hamazon but not birkat "Al achilat matsa". He refutes this svara, because BHM is a mitsva as well. So one cannot bless neither birkat al achilat matsa nor birkat hamazon. Just to be clear, assuming that one need to bless birkat hamazon, this doesn't imply that one need to bless birkat Al achilat matsa. Birkat hamazon is different from "Al achilat matsa", BHM is a mitsva about satiety state, but not an independent duty, note that it's nusach doesn't contain "asher kiddeshanu...". It's a "result" of eating, a mitsva to thank for satiety. Anyway, the Yerushalmi unanimously taught that there is never bracha for achilat matsa, and even if there is bracha on food.
Maybe that I missed details, if something is wrong, I will be thank if someone reports an error.