This is a nice idea. Much of physics has been derived from symmetries/conservation laws (see noether's theorem), which seem to be related but not identical to c

This is a nice idea. Much of physics has been derived from symmetries/conservation laws (see noether's theorem), which seem to be related but not identical to counterfactuals. For example, spatial translation symmetry directly results in the conservation of linear momentum, which then implies that certain types of scattering scenarios are physically impossible. It's an interesting thought to try to go the other direction. It isn't clear to me that the chain of logic above would necessarily be bi-directional for all symmetries/conserved quantities/counterfactuals.