Where are you from? I am in Bogotá
(please per PM)
In the french-classic organ, till Cavaille-Coll, the Grand-Orgue-cornett ist meant to counterbalance the weakness of the trumpet 8 in the discant. Due to metallurgy in these old times, it was not easy to have the desired trumpet sound till the highest of the Keyboard. So the cornett begins in piano at midle c and wins power where the trumpet looses power. Try trumpet with cornett to hear this.
The french classic organ has codified the registrations (fugue sur la trompette, Grand-Jeu etc) with trumpet that uses the cornett in combination with the Tp (and with the prestant too).
Furthermore, the G.O.-Cornett is not really intended to be heard alone (but you can do it of course).
So yes, this is from birth, this not a problem but a solution.
The equivalent of the cornett in little-sized french-classic organs is the jeu de tierce of the 2nd manual: Bourdon-Prestant-Nasard-Doublette-Tierce. Flute cornetts appears in bigger french organs
To have a full cornett, try the Pitea-organ from Lars.