Well
Sol Steinmetz, a renowned linguist, cites
Peg and
Peggy as examples of how language has evolved from baby talk.
https://books.google.com/books?isbn=0307496465
I have also read other books that have referred to it. I'm going to take his word for it over a journalist on Mental Floss who doesn't cite his sources.
I also wasn't disagreeing with the all of what you said. Just that they didn't randomly decide to replace letters. The replaced letters did stick though because there was a lack of variety in names.