I would say that the logic behind this design is sound from an Information architecture point of view so you are right in pointing out that:
I can take a good guess as to why this is the case (reduce level of
cognition, reduce choice, promote certain sub-categories).
I would add that the design follows a number of Information architecture principals :
The Principle of Choices as outlined below :
The Paradox of Choice is a book by Barry Schwartz  that came out in
2005. In brief, the book’s message is that a greater number of options can make it more difficult for people to make a decision. More options
means more cognitive effort, and more effort can sometimes mean more
anxiety. People think they like having a lot of options, but they
really do not.
So your guess is spot-on, presenting the user with too many choices overwhelms the user and causes cognitive overload.
The Principle of Exemplars as outlined below :
Describe the contents of categories by showing examples of the
You are also right on this one, by showing number of sub-categories the designer is showcasing examples of the products to improve user understanding of what this category includes.
Last but not least: The Principle of Progressive Disclosure as outlined below :
Show only enough information to help people understand what kinds of
information they’ll find as they dig deeper.
By showing a limited number of products under each category the designer is setting users expectations of what they will find if they dig deeper while also providing a link to most visited sub-category pages.
With regard to "view all" link i think its part of the progressive disclosure approach as users are guided to take action once they have understood what each category includes.
I would end with this quote which sums up things quite well :
Information presented to a person who is not interested or ready to
process it is effectively noise.