Children start with a very limited vocabulary: exactly 0 words. From there they learn new words to add.
They learn words faster if they are used more often. Additionally, "Mommy", "Daddy", "[child's name]" are words that are highly important.
3 words: Mommy, Daddy, [child's name]
More than 3 words: I, me, mine, myself, my, you, your, yours, yourself, he, his, himself, she, her, herself, they, theirs, themselves.
The example by the OP is about crossing the road. This is a situation where it's important the child understands what is said, so parents tend to use words they know the child understands.
Occasionally, while the child grows up and learns, parents can be a little slow in adjusting their language appropriately. At the start the child will not understand the parent unless simplified language is used, which is a strong incentive to use simplified language - the incentive to use standard language as the child grows up is far weaker.
P.S: The truth is not that simple, because not all words are equal. Nouns that refer to whole "things" (e.g. "Daddy", "hand", "road") are easy to teach and learn - you can point at them and say the correct word. Verbs are less easy, pronouns and abstract nouns (e.g. Acquisition) are hard.