If you can engineer transmission of information faster than the speed of light, you can violate causality. On a small scale, that means acausal computing in which results can be generated before inputs, thus allowing for infinite processing power per unit time. On the large scale, outright paradox in the form of event chains that prevent their origination. These outcomes would be problematic to account for in our understanding of physics, to say the least, and seem like a better argument than others for assuming that FTL and all things that would enable it (e.g. sufficient amounts of negative mass) cannot exist.

It remains an interesting challenge to prove that more rigorously, of course.