The 5.7 MMJ has the advantage of using standard magazines and not requiring mods to gas system. BUT - performance ain't all that wonderful, though as Frank Barnes notes, it is efficient. 40 grain HP with 14 grains of 4227 makes 2850 fps; 40 grain HP with 12 grains of 2400 gets 3000 fps; 50 grain HP with 14 grains of 4198 makes 2700 fps.
So - been tried, works, but not so well as to become a popular thing, factory or wildcat. In a carbine, it throws brass all over hell's half-acre, so it tends to be expensive to shoot due to brass loss. I have thought it ought to work well as a conversion in a Ruger 22/77H, what with the rim diameter on the Carbine case being almost exactly the same as a Hornet. Might need a little rotor alteration on the magazine because the case body is fatter, but not that much. Never had enough money to play with the idea.