I know way back when, we had schools that focused more on teaching a singular classroom vs an entire school that taught several classrooms. Why were public schools created and introduced to begin with?
They started as a means to provide more students with more educational options under one roof. The first one created in the US was in 1635 and is still standing today, the Boston Latin School.
I didn't know the first school that was built is school standing today, that is impressive! As mentioned it was meant for children to be better educated for the benefit of the country and the economy. It also allowed children to become adults and have as many opportunities as everyone around them.
If you think back to the first few schools, it was often a mother or young woman without kids of her own teachers a small class room of kids. As the populations grew, they needed to seek out better options to house more kids and provide more teachers the opportunity to teach.
So there can be a state run educational system ensured to reach as many children as possible. The big drawback of that though is states and areas that struggle with money get shafted and the schools are a dump.
To ensure that all parents had access to education no matter what level their income was. Since most public schools are free outside of supplying school supplies and charges for field trips, parents are able to ensure their kids get educated.