Wow, that's different side of the story I do not hear often. I am a deaf child of hearing parents. As soon as they found out that I am deaf, they hired someone to teach us sign language. It's not ASL but plain sign language. I love to read when I have spare time, mostly because my parents will sit by me at night and read books to me while I was really young kid. So I basically grow up being surrounded by books and love for books.
I grew up having a mixed sign language (somewhere between ASL and SEE) and that's not a bad thing. I do not mind it, because that's what I liked, getting a best side of both worlds. I love English, but yet enjoy ASL.
I am just lucky that I come from good family which is very willing to learn sign language and started training me on reading and educate me at very young age, pretty much like what hearing parents do with hearing children. So I am being able to move at the same pace as hearing children do. Even though I move at the same pace, I am still little weak at both language (English and ASL) because I do not get to hear English at all and do not get to see ASL all the time. More I use it, better I get at it. It's all about train yourself. Deaf people are capable to learn at same pace as hearing people do, just they use different system that's all.
It's all depend on parents if they are able to communicate with children and develop language for children at critical period of their life. Once child pass that critical period without learn any kind of language, child may be doomed to lag behind hearing children for rest of his/her life.