Why is a birkat mitsvah not recited upon performing the mitsvah of the recitation of birkat hamazon? This would perhaps be akin to the blessing upon Bitkat Kohanim as noted by @danno.
This is discussed in the Sefer ליקוטי שושנים on page 13.
Essentially he answers:
Since we bless Hashem during the Birkat Hamazon (Grace After Meals), there's no need to first bless Him before doing the Mitzva.
There's no need to make a Bracha on a Bracha, since the point of making the Bracha is taken care of as we say the actual Bracha.
Similarly we don't have a Bracha upon reciting Kriat Shma, since Shma is all about accepting the yoke of heaven, making the pre-blessing redundant.