Views lang. acq. within the context of the child's broader intellectual development. A child first becomes aware of a concept, such as relative size, and only afterward do they acquire the words and patterns to convey that concept. Simple ideas are expressed earlier than more complex ones even if they are grammatically more complicated-- Conditional mood is one of the last. (cf. Spanish vs. Russian.)
There is a consistent order of mastery of the most common function morphemes in a language Example from English: first-- -ing, then in and on, then the plural -s, last are the forms of the verb to be. Seems to be conditioned by logical complexity: plural is simple, while forms of the verb to be require sensitivity to both number and tense.
Pros and cons-- clearly there is some link between cognitive development and language acquisiton; Piaget's theory helps explain the order in which certain aspects of language are acquired.
But his theory does not explain why language emerges in the first place. Apes also develop cognitively in much the same way as young children in the first few years of life, but language acquisition doesn't follow naturally from their development. Bees develop the cognitive ability to respond to many shades of color, but bees never develop any communication signals based on shades of color.