The description of Nature requires handling of non-conservative, non-closed physical systems without known inertial conditions. This problem can only be solved within the Lagrangian formalism, for instance in order to get the equations of motions.
The Hamiltonian formalism which is based on energy expressions and on energy conservation is not able to deliver the handling of such important physical problems. For instant, I use only the conservation of elementary charges instead of the conservation of energy. No, H is not more fundamental and not more general. I use neither E = hν, nor the energy mass equivalence principle E = mc^2.
My theory is a quantum field theory with only quantized charges as the sources of the interacting fields. The energy is not quantized.This new quantum field theory has unified the electromagnetism and the gravitation. The interacting fields propagate with c.
The gravitation is neither universal mass attraction, nor it is a deformation of space-time. The gravitation is caused by conserved elementary gravitational charges of stable particles. And the gravitational masses are different from the inertial masses of bodies.