That happened to me when I was a child. I didn't lose any baby teeth naturally. I knocked two out on a sandbox. The others all had to be pulled because my permanent teeth were all coming in very crooked and my baby teeth would not come out. So, I spent a lot of time at the dentist getting my baby teeth pulled. There is a good and bad side to this. The good side is that they were able to pull them so that my permanent teeth came in beautiful and straight and I never had an overbite or had to wear braces. The particular problem ran on my mom's side of the family and they all have these ugly overbites and horribly crooked teeth. The have more cavities because they can't clean between their teeth well because of the crookedness. When my little brother had the same problem my mom didn't have the money to do the same thing as with me. So, when he hit his teens he had to have braces and have the overbite corrected which was painful and embarrassing for him.
The con for me was that I was kinda traumatized by having my teeth pulled. But then again, my dentist was this huge, loud man. I think he scared me more than having my teeth pulled! But then again...I think that experience made me better able to deal with pain. I have no problem dealing with needles or any other pain now. People are amazed by it. I really do think it's because I had all the dental work back then.
Overall I'm glad it was done because I have nice teeth. And I didn't have to have braces or have an overbite corrected like my brother did.