Puzzles do help a lot children who have problems with concentrating and problem solving. My son started going to Mommy and Me classes at age 3. We were in a group with mixed age children and there were some who could not concentrate and had delays with their developing. So by means of puzzles and big blocks some of those children got so interested and could solve the puzzles and be able to concentrate on their given tasks.
Comprehension is an important part of the cognition since it teaches children to be able to determine the meaning and be able to understand better and be more clear. And you are absolutely correct; the combination of both cognition and comprehension gives a wonderful outcome for a child to be able to use his or her speech and be productive with it.
Children learn more than we can even imagine that is why we must never stop teaching them and working with them while we can. Since children have the tendency of learning more than adults can; for example it is easier for a child to learn a different language than for an adult.