I think I was a little slow, or at best normal in picking up reading as a kid. But for whatever reason, by about the age of 8 I was reading well ahead of the rest. So I never read The Cat in the Hat, but I read the The Hobbit long before most kids.
And I'm glad, because that second level is where the real power-tool lies. There's little point reading non-fiction at Cat in the Hat level. But there's plenty of facts available that are simpler to read than The Hobbit.
That isn't to say I didn't learn other stuff: my favorite childhood book was about science. But it had lots of pictures, and when fist got it, my parents read an explained it to me.
I was very happy to read early, and I think it was advantageous for me, but I have not seen evidence that early reading in itself provides any lasting advantages on average. There may be a good deal of heterogeneity in the early-reading population.
When we taught our own kids to read, I was surprised that this was not the way that they would learn to read. We ended up having good success with hooked on phonics with our first two and the last one did well with vast amounts of repetition and memorization of his favorite books.