The doll probability might possibly remind you of another "maddening" distribution... GB BPs.
Just the way it is. However, there are reasons Inno does this.
If the BP placement probability for each cell of the 9-cell matrix was a uniform distribution (Gaussian) , it would dramatically cut down on a player's requirement (need) to keep going back to get more prints, and change the entire early game dynamics. While it's a pain, it's required to keep the game moving, and yes - even sell BPs for diamonds, a revenue source.
Same for the "frustration" on missing dolls.