Indeed, -- the Eucharist is the kind of food from which the flesh does not profit. Yet, it is Hs flesh and it is "food indeed". This is the Real Presence as the Church teaches it.
This “transubstantiation” dogma is the thing that is a late-comer
Transubstantiation is a way to explain the Real Presence in the light of modern (that is to say, Medieval) philosophy. It is indeed a medieval construct, not terribly popular in the East either. But the real dispute is the Real Presence of Christ in full in the Eucharistci meal. That is taugth directly in the Bible. There are allusions to the transubstantiation as well, but they are more subtle.
That is one of the reasons why I reject the theory (made dogma) of transubstantiation.