When I have was taught quantum statistical mechanics, the course derived the canonical ensemble by assuming that eigenstates of the total system Hamiltonian have equal a priori probabilities, and then imposing Lagrangian constraints for the average energy and sum of probabilities being equal to one.

I want to know, why **physically** it is the eigenstates of the Hamiltonian that should have equal a priori probabilities and not some other complete set of states that span the Hilbert space?