You seem to know more about this than me, but it seems to me that the first law does more than just induce a metric, I've always thought of it as positing inertia as an axiom.
There's also more than one way to think about complexity. Newtownian mechanics in practice requires introducing forces everywhere, especially for more complex systems, to the point that it can feel a bit ad hoc. Lagrangian mechanics very often requires fewer such introductions and often results in descriptions with fewer equations and fewer terms. If you can explain the same phenomenon with fewer 'entities', then it feels very much like Occam's razor would favor that explanation to me.
There's also more than one way to think about complexity. Newtownian mechanics in practice requires introducing forces everywhere, especially for more complex systems, to the point that it can feel a bit ad hoc. Lagrangian mechanics very often requires fewer such introductions and often results in descriptions with fewer equations and fewer terms. If you can explain the same phenomenon with fewer 'entities', then it feels very much like Occam's razor would favor that explanation to me.