Okay, though public school interactions might not be the best form of socialisation for the development of a well-rounded individual.

This is an important point. School is super fake. There's no other time in life when you're rigidly segregated by age and only have people with as little experience as yourself to learn from.

It's common for homeschoolers to make sure their kids interact with younger kids, older kids, and a variety of adults. Some schools make a point of this too, like Montessori.