It has about as much impact on perceivable tone as an expensive so-called Bumble-bee cap swap in an electric.

Translation - if someone is keen to buy into some of the assertions of the snake oil sales folks one may perceive a profound difference too from one rod to another. If not..... not so much.

What do I think? Sure there may be some differences because of differences in mass, how large the channel is and subsequently how much material is removed or not, etc. But if there are any differences I have yet to hear anyone proclaim that "this rod sounds better than that rod." I'm sure though that if we asked enough folks someone would have a favorite "tone-rod."

For me I select rods based on functionality and reliability and never tone. How would we possibly know and tone is subjective as all get out.