I'd figured it a good deal differently then that, and for that reason, don't see the issue.
Basically, the procedure is done perhaps even before childbirth, if the icon is anything to go by. The new child doesn't lose their sense of self by inheriting the memories, and I do see it like that. Its not the child having their consciousness erased and overwritten by another, they simply inherit the memories, likely often with built in conditioning that protects the child from those memories. It would be like me waking up every day with a few more memories of my grandfather's life. I wouldn't become him, I would still be me, but I'd have his knowledge, experience, and wisdom, which I could then choose to completely ignore.
With Arci I wrote a very clear divide into her mental state. She's 29, she has physical memories of those 29 years of her life, and despite having had memories of her past lives slowly trickling into the back of her mind, she still manages to be a normal kid, make stupid decisions, and get in trouble for them. Her memories are very much just that. Memories. She's not the same person any more, and some people who were best friends with her in a past life probably don't like her very much now.