No argument here AB, this is totally for the sake of discussion. I'm pretty sure the "main" function of the spider is to keep the coil centered in the gap. However, that is certainly not the spider's only function. I do agree with you that it is also responsible for returning the moving assembly to the "home" position. Consider also that in some cases the spider is also known as the damper.
It will be interesting to hear the engineer's perspective, and i truly appreciate you asking and sharing.