In support of your idea, engineers routinely use FEA simulation software that models dynamic systems without any explicit representation of angular momentum or

In support of your idea, engineers routinely use FEA simulation software that models dynamic systems without any explicit representation of angular momentum or rotational inertia. Only linear displacement/velocity/acceleration, "translational" mass, and elasticity. Such software can still model rotating systems and all the complex effects that come with rotation. So at least classically, I don't think angular momentum is a fundamentally essential concept.