Jeff and Nima
Thank you for your time and scenes. Sadly, maybe I'm wrong, it seems both solutions are the same thing I've shown on my second post

My issue with this workflow is that:
- It's “dirty” since I'm creating trash attributes I don't need.
- I'm not processing all groups automatically and have to micromanage it.
I see both of you using
Attribute Create and I'm wondering why use it instead of Attribute Wrangle for this case or what are the advantages over the wrangle in general. I'm not Houdini old school

@Nima
I'm not after coloring stuff. Used it here just as a display mechanism but thank you for highlighting that is possible to use expressions with it.
@Jeff
I'm not settling with this answer, I'll RFE x) I think either
Copy to Points could drain groups from which geometry elements the copies are paired with, or…
Maybe
Group Transfer could have an input where an attribute can control the mapping of the source elements to the target elements, since there's a mapping going on with its “search” but it's blackboxed, so this new input would override the Search and maybe be faster. This solution might also have broader and more abstract applications beyond solving
Copy to Points group transfer.
So, which is a better RFE?
Copy to Points to transfer groups or
Group Transfer mapping input?
Mockup of proposed Groups Transfer workflow:

I can see the similar mapping mechanism being further used to also transfer in mass things like primitive and vertex attributes which are atm ignored in operations like
Copy to Points, etc.
As for the edges… yeah…