No, not all children acquire full competence in their L1 for various reasons, and yes SES can be one of the factors, but there isn’t much research on this topic. I am not saying poverty always affects linguistic competence, no, but it can be one factor in causing a delay in language development.
If you’re talking about acquisition of L1, yes some children have delays. If you are talking about intelligence and how well they do in school, that’s a whole different sphere and I’m looking at them separately. Language acquisition does affect intelligence and how well they do in school (without a strong L1, they will struggle), but someone could have a strong foundation in L1 and still not be intelligent, or do well in school. It’s not correlative both ways.
If you want to read the research—the introduction to this one is a good summary
Then there’s this excerpt from a very mediocre article on wiki “language delay” there’s one part that I’ll quote here:
Language delay is commonly divided into receptive and expressive categories. Receptive language refers to the process of understanding what is said to us. Expressive language refers to the use of words and sentences to communicate what we think, need, and want. Both categories are fundamental in order to be able to communicate with others as well as to understand when others communicate with us.
Language delay is a risk factor for other types of developmental delay, including social, emotional, and cognitive delay, though some children may grow out of these deficits, even excelling where they once lagged, while others may not. One particularly common result of language delay is delayed or inadequate acquisition of reading skills. Reading depends upon an ability to code and decode script (i.e., match speech sounds with symbols, and vice versa). If a child is still struggling to master language and speech, it is very difficult to then learn another level of complexity (writing). Thus, it is crucial that children have facility with language to be successful readers.
Neuroscientist Steven Pinker postulates that a certain form of language delay may be associated with exceptional and innate analytical prowess in some individuals, such as Albert Einstein, Richard Feynman and Edward Teller.
In 2005, researchers found a connection between expressive language delay and a genetic abnormality: a duplicate set of the same genes that are missing in sufferers of Williams-Beuren syndrome.
To finalize my point with something way less academic, I work with kids with L1 delay everyday. It’s my job to get them caught up on L1 delays AND acquire L2—and yes, I’ve seen the impact of SES on their education and whether they recuperate the delay, same as in other areas of education.
Also- to answer your last question—yes, many (not all) of the L1 delays that I’ve seen are because of inconsistent exposure to language, but again, there are some exceptions where the L1 delay is caused by something else.