Your reasoning is essentially correct, and that kind of thinking is part of what got us from Newtonian Mechanics to more advanced physics. If you look at Lagrangian Mechanics, Classical Field Mechanics, or Quantum Field Theory, you deal primarily with energy and momentum - the conserved quantities. Forces can be extracted from solution if you need them, but the concept of a "force" is not directly used in solving a problem.
If you look deeper, into things like Quantum Electrodynamics and Quantum Chromodynamics, you see that even conservation laws aren't fundamental. What's fundamental are certain symmetries. From each fundamental symmetry arises a conserved current and gauge fields that carry forces. So you end up with both conservation laws and forces as a consequence of symmetries. The mathematical formulation of this comes from Noether's Theorem.
In classical physics, invariance of the laws of physics under translation gives you conservation of momentum. Under time - energy. Under rotation - angular momentum. Since only global symmetries are considered, you don't really get a gauge field.
In Quantum Electrodynamics, the U(1) local symmetry gives you both the conservation of electrical charge and the electromagnetic forces that couple to this charge.