I believe the distinction in the literature between wave-function methods and DFT is slightly different. In my understanding, the distinction is not that in DFT the energy is actually calculated from the density, once we know the density, because the question remains how to find the density. Rather, the distinction is that in DFT the solution to the electronicstructure problem is obtained by minimizing a total energy as a functional of the density, while in wave-function theory the solution is obtained by solving Schrödinger's equation. So, calculating the energy from the density does not mean literally plugging the density into some orbital-free expression, but the process of minimization of the total-energy density functional to obtain the minimum value, which is the total energy of the interacting system.