A few weeks ago I asked why it is that we go out of our way to wear a 4 cornered garment to be able to fulfill the mitzvah of tzitzis but no one makes a point of washing every meal in order to have the opportunity to fulfill the aseh of bentching.
My bad for not remembering that my wife's grandfather, R' Dov Yehudah Shochet, dealt with a similar issue. He suggested that even though technically one is not required to wear a 4 cornered garment, the way the Torah phrases the mitzvah alludes to the fact that one should do so. Tzitzis is phrases as a command, gdilim taaseh lecha. The mitzvah of maakah, by way of contrast, is conditional, ki tivneh bayis. Same with shiluach ha'kan, ki yikarei...
I did not pose an answer back then, but was thinking that birchas ha'mazon is different because the mitzvah is to give thanks. You can't force someone to give thanks or order then to give thanks. It's an emotional response that a person has to feel. Therefore, we cannot require someone to fulfill the mitzvah of bentching in the same way we require wearing tzitzis.
Minchas Chinuch and others discuss whether one can fulfill the mitzvah of mikra bikurim through shome'a k'oneh. One aspect of the debate relates to the disagreement between Beis haLevi and Chazon Ish whether birchas kohanim can be fulfilled through shome'a k'oneh. Beis haLevi held that since birchas kohanim must be said b'kol ram, it must be heard, therefore shome'a k'oneh does not suffice. We do not ascribe to the listener the properties of the "voice" of the speaker. C.I. disagreed. Here too with respect to mikra bikurim, Rashi comments on v'anisa v'amarta that one has to say the declaration out loud. However, I think there is an additional issue here. Avudraham writes that we say modim derabbanan during chazaras hashat"z and do not simply listen to the recitation of modim by the shliach tzibur because modim is an expression of thanks, and thanks has to come from your heart. It's not about saying the words; it's about feeling the emotion behind them. Similarly, mikra bikurim is thanks to Hashem for the harvest. Here too, someone cannot stand in your place to experience that emotion. The words are just an expression of what one has to feel in one's heart.