The power of play is an intriguing element in children's literature and its influence appears to be stronger than we may initially presume. Today, let us wade through the depths of imagination and explore how children’s books leverage the psychology of play to foster learning and growth.

The Role of Play in Children's Literature
Play is an integral part of a child’s development, stimulating cognitive processes and bolstering emotional dexterity. Beyond just fun, play serves as a window in which children begin to comprehend their world. Children's literature taps into this tool of play to communicate complex ideas, emotions, and experiences. A good example is 'Where the Wild Things Are' by Maurice Sendak, which beautifully illustrates a fantasy play drawn from the emotional whirlpool of a child’s mind.

Symbolic Play Corners within Storylines
Symbolic play is a critical aspect of a child’s cognitive development, paving a pathway towards creative thinking and problem-solving skills. Peter Pan's Neverland or the magical wizarding world of Harry Potter present perfect zones of symbolic play, providing children with a context where they can redirect their realities into imaginative arenas.

Riding on Active Play
Active play in children's literature takes the form of adventurous quests, solving mysteries or overcoming obstacles. This stimulates a child's drive towards action, competition, and skills enhancement. 'Treasure Island' or the 'Famous Five series' tap into the aspect of active play, not only providing an outlet for children’s adventurous spirit but also fostering the growth of resilience and determination.

Creating Through Constructive Play
Constructive play engages children in designing, building, and creating, promoting their logical and analytical abilities. Literature allows for mental models to be constructed through intricate narratives. Books such as 'The Very Hungry Caterpillar' or Dr. Seuss’s range stimulate this form of play, enabling children to construct and gain knowledge about patterns, sequences, and transformations.

In conclusion, the usage of play in children’s literature is not mere coincidence – it’s a purposeful strategy. It integrates cognitive, emotional, and sociocultural theory aspects, offering a compelling perspective into the influential role that the psychology of play holds within children's literature. This 'literature of play' moves beyond merely reading words off the pages, allowing children to interact, imagine, and learn from the narratives. So, as we flip through pages of children's books, let's remember the importance of recognizing and promoting this universal language of play - a 'child's work' indeed.