Well, what is fundamental isn't the point. If you imagine a world where different quantities are conserved, there would no doubt be different change-of-frame equations describing how they are. The point is you can imagine a world where energy is conserved but momentum is not. Actually it's possible to imagine physical systems, with affine frames of reference, where nothing is conserved at all.
Fundementality is a different thing, but it's more natural to assume conservation laws and take frame-of-reference equations are a consequence. You can do it the other way (I'm pretty sure, but not 100% sure because my physics math is rusty) but you're still making assumptions, and you still don't have one conservation law following from the other.