Having read about some of the history of this idea, it seems to have been originally built on philosophical grounds, the idea that nature chooses the most harmonious path, as opposed to Newton's laws which seem to come from intuition based on observation of the world. If you keep asking "why?" in either framework you will eventually run up against an epistomological barrier which is unlikely to ever be crossed but in the case of Newton's laws, their basis in physical intuition makes them much easier (for me at least) to accept as given and take as a starting point for constructing a world model. With this being the case I think an acceptable result for me would be to find a proof of equivalence between the Newtonian and Lagrangian pictures. From my reading it seems like the derivation from D'Alambert's principle may be part of the journey.