I applaud the effort here. But I don't think you can assume an equal distribution amongst the leagues. It's just easier to run bots in bronze and silver. In the higher leagues you see more of the customized bots. In bronze you see the generic bots people rent from the big suppliers. They can just play the ghost cards and rent any cheap card for CP.
There are also just a much larger sheer number of accounts playing bronze and silver.
Also, I now rent out $75k worth of cards. I can tell you that they rent in chunks all at once to numbered players and I'd say that over 90% of the cards I rent out are never played. Bots are probably over 300k of the active players. Just bots renting for CP
Probably the method as mentioned is very much simplified.
however, one thing makes it a bit trustable - I'm in the Gold II which is at the median position among all leagues.
I gave it another thought as what you mentioned, the distribution. I think the distribution for Bots, rental account and card owner account pretty much different. I would say something in below picture. it could also different from it depends on the profitability. since i did not see the bots/rental account at Gold II compared to Bronze, so i believe below distribution is still valid in a certain way.