But why do they need this from public school over say any other social ... activity (?). For example sports.
I am genuinely questioning whether public school makes children socially mature rather than only being a traumatic experience for many pupils, for no other reason than that public schooling is the default choice.
No you're right, there is no other reason than public schooling being the default choice. Which is why its necessary. It's self fulfilling.
It's the choice that everyone goes through. So unless you want your children to be unable to adapt to the people that were shaped through that horrible system, you will need to introduce them to that system in some capacity. Sports are not really enough. School is like day job for kids until they're 18. Everyone goes through the same standardized garbage, and they will have to live their lives with other people who went through the same standardized garbage.
Your only choice is to pay exorbitantly so they don't go through that garbage, but will face adulthood with 99% of the population that did, which can have mixed results.
What school does is provide an environment of ~8hrs/day to pressure test their social skills and build coping mechanisms (good and bad). You do get that to a lesser degree from other environments such as sports and in the end it's all transferable learning. Playing on a team vs training an individual sport with a club gives very different social lessons and shapes them accordingly.
But I don't think school is what makes them mature as much as it's the adults that they look up to and emulate that shape that. And whether it traumatic can depend on how they're able to internalize it.
I am genuinely questioning whether public school makes children socially mature rather than only being a traumatic experience for many pupils, for no other reason than that public schooling is the default choice.