You are correct. I majored in educational psychology and this language development in children has always been a special interest of mine.

Baby talk is like beacon to the baby, it tells them that "This is for YOU, pay attention!". The baby hears and learns the intonations, patterns and the rhythms of the language. It's importance cannot be downplayed.

A toddler can learn ~50 new words every day, so using normal speech is naturally important as well. But there is no need to try to overdo it. The mind of a small child is a massively powerful and superfocused "learning machine", although it isn't often apparent in their behaviour ;)

Reading to children is especially beneficial to language development. It enriches the vocabulary and introduces common patterns and rhythms of expression. And the pictures in books help to create connections between ideas and words.

The pace of language development is highly individual and forcing it is most likely useless. Children will learn what they can, at their own pace.

Every one of my own children were able to use polynomial sentences and past and future tenses before they were three. We never tried to accelerate their learning in any way, they just picked it up. On the other hand, my friend's kid did the normal baby talk phase and then remained completely mute until the age of four. One day he just opened up and said to her mom in a clear voice: "Mom, could you give me some milk, I'm thirsty." And he spoke normally ever since.

One advantage of quick language development is it's effect on memory. A child that learns complex language skills early is more likely to form lasting memories of their early childhood. It may be that the memories can be stored more effectively and recalled more easily when the child is able to bind the experiences to words that can be used to express them.

This is a very fascinating subject.