It would be redefining the unit though. For example we define 1 Newton as the force to accelerate 1KG by 1m/s². We could alternatively define it as the force between two 1KG masses 1 meter apart or between two 1Coulomb charges one meter apart. In certain ways they are better definitions since they a fundamental property of the universe. Could you clarify though why wouldn’t energy in the new unit defined as 2mc²? Do agree what you’re saying with regards to formulas have a meaning. And it is definitely amazing how you lead up to formulas