The tool’s purpose is to aid in gaining an even surface, prior to tamping.
In an extremely finicky and complicated nutshell; an evenly dense coffee-puck, is going to give you a more balanced, higher extraction.
How is this different to other distribution methods?
Example: a café has 4 different baristas on bar throughout the day, all have different experience, different technique, different heights, skills, knowledge… list goes on… Even a barista can distribute many different ways throughout the day. Using a re-distribution tool, ensures more consistently extracted espresso.
Teaching beginners good habits.
Do you remember a time where you would spray grinds in to your basket and tamp them with all your might? Well, we know we have all come a long way in coffee (and still have a long way to go) so having a tool in place to demonstrate the idea of even density, is something we advocate.
Re-Distribution. Meaning, check your initial distribution!
The biggest thing that many users discount is the way in which the coffee is delivered into the basket. (Initial distribution)
For example, if your grinder is delivering the grind into one corner of the basket, the density in that area will increase and adversely the density in the other areas of the basket will decrease.
Attention must be paid to the way the coffee falls into the basket and must be cared for and coaxed into an even delivery where possible, regardless if a re-distribution tool is being used or not. A distribution-tool is not going to make a difference if you are not considering these things first.