Generally no, there is no reason to have all the same. But on the other hand I finally ended up with components of great sound quality from the same company which required neutral passing of the signal so, it pointed to the same neutral interconnects.
If you are able to get to a really high end series of components that are compatible… then the solution becomes transparent communication of the signal. In that case a single weave makes sense.
I have fooled around with interconnects and cables for many decades. When your components have different strengths or character you are trying to tune your system (make up for individual shortcomings), if your components are compatible and synergistic, then all you want is transparency.