I answered a previous question that gets at some of the history around the development of playgrounds. As to why those three things, they were seen as essential components for a gymnasium.
The originator of a space designated for children to play is generally recognized as Friedrich Froebel, the German creator of kindergarten. The first playgrounds were in Berlin and were piles of sand in public parks, inspired by Froebel's notion of "gardens" for children to explore. A group of women philanthropists took the idea from Germany and had a pile of sand set up in a Boston neighborhood in 1885. Their goal was to provide a clean, safe place for poor, immigrant children to play and a way for them to learn social skills considered important to being an American. From Lange's^1 history of the playground:
country children had plenty of dirt, while wealthier city children likely had yards; it was poor children who needed access to free, communal play spaces. (page 205)
As the sand pits became more popular and crowded, community leaders moved them from street lots to spaces near schools. As a result, they moved from the supervision of women's groups like the Massachusetts Emergency Hygiene Association that created the original ones to school boards and the city parks department. In 1889, the city opened an "outdoor gymnasium" which was the first of what we think of as a playground - an outdoor space set aside for children to play on apparatus (swings and seesaws). Jane Addams, the reformer and creator of Hull House in Chicago was a founding member of the Playground Association of America^2 (PAA), built a similar playground for the children at Hull House. Rather quickly, the idea of playgrounds, an area of land set aside explicitly for children to do the work of play, spread across the country.
The design of playgrounds around the turn of the century was deeply informed by how educators and others were thinking about stages of childhood. NYC built sand "gardens" for toddlers, areas with sand, swings, seesaws, and wheelbarrows for "little boys and girls" while NYC's "playgrounds for big boys" (AKA teenagers, though that wasn't really a concept yet) had adult-sized gymnasium equipment and walls for handball.^3 In 1911, the PAA would change its name to Playground and Recreation Association of America, reflecting the growing interest in not just the spaces children played in but the things thing did in those spaces. Playgrounds were often lit at night, allowed adults to use the equipment, and staffed by women, known as matrons, who supervised play.
At this point, it's necessary to pause and drop the name G. Stanley Hall. Hall, a white psychologist, created the idea of "child study" and even by the standards of the era, was exceptionally racist, sexist and ableist but also a strong advocate for protecting childhood and not minimizing the contributions of (white) children and the (white) elderly to society. He was socially connected and highly sought out as an expert on childhood. Which means his fingerprints can be found all over child-related topics in the early 1900's. He believed passionately in the need to separate children by their age and advised groups from the YMCA, city parks organizations, and school superintendents and leaders to take actions towards that goal. When it comes to playgrounds, his influence - for good or for bad - can be seen in schools with a little kid and big kid playgrounds, with spaces that have side by side big and small slides or swings, and spaces that strictly controlled what girls could do while giving boys free-reign.
Like most things involving American children, race played a factor in who got to play on what and where. Booker T. Washington wrote editorials calling for access to playgrounds for Black children while others used the concept of play as a way to argue for desegregation and integration. Playgrounds for white or Black children typically had the 4 S's (swing, seesaw, slide, sandbox) but the quality of the equipment varied based on location and the race of the children using them.
Regarding the source of the equipment, most of it came from indoor gymnasiums but some pieces were built specifically for children. A great deal of the equipment, including many of the pieces featured in Biondo's collection of photographs^4, came out of an adult's imagination about what children would want to play with and on. (Adults who watched said children play had very complicated feelings about said play. Some feared swinging too high was too vigorous for girls' bodies while others believed all of the spinning, climbing, and time in the fresh air was good for children's lungs, brains, and muscles.) The idea of the jungle gym came from a patent lawyer in Winnetka, Illinois. He'd grown up in Japan and his father, a mathematician, made a bamboo frame to teach geometry but found that children preferred to climb and sit on it.^1 The Winnetka school district had a focus on play and the lawyer met with the superintendent to share his idea. They built a prototype, the lawyer founded a company called Junglegym, Inc., and an American playground staple was born.
The end of the that-slide-is-stupid-high-and-those-swings-are-deathtraps playground came in the 1970's when consumer safety advocacy groups gained steam and parents filed lawsuits on behalf of children who had been injured on playground equipment. School district insurance providers threatened to withhold coverage unless the schools updated the equipment or made the space safer. Each decade has brought a new tension related to the spaces set aside for children to play and the conflict between fun and safety, between independence and control.
Lange, A. (2018).The Design of Childhood: How the Material World Shapes Independent Kids. Bloomsbury Publishing USA.
Playground Association of America (1911). The Playground. Volume 1, Number 1. (N.B.: unsurprisingly, the journal leans heavily on racist narratives of Native and Indigenous Americans.)
Chudacoff, H. P. (1992). How old are you?: Age consciousness in American culture. Princeton University Press.
Biondo, B. (2014). Once Upon a Playground: A Celebration of Classic American Playgrounds, 1920-1975. ForeEdge.