The four-momentum of a physical system is a conserved quantity in a particular reference frame. But we need a relativistic invariant theory which doesn't depend on the  choice of coordinates. The squared four-momentum is a [scalar invariant][1], i.e., it doesn't depend on any reference frame. Thus a relativistic invariant theory requires a formulation based on invariant quantities.


  [1]: https://en.wikipedia.org/wiki/Lorentz_scalar