You can easily rectify that through community activities, sports, church; there's a plethora of ways to deal with that. Some public schools do very well. My kids went to a great elementary school that was very diverse. Within a year after the last one left, it sunk to rock bottom. They fired the principal because of the low test scores, though he had successfully navigated that school for decades. I'll give you three guesses as to how the demographics changes, first two don't count.

I remember the last public school function as very different from the first. First, everyone sat in their seats and let the kids do their thing. We all got our pics and had a great time. Last time? A whole slew of people were late and didn't want to sit in the back so they milled in the aisles. One guy marched right up front to stand directly in front of his kid with a camera to film them and blocked everyone else. The principal even had to stop the performance and lecture everyone to behavior better than their kids were. Last one for me and thank god it was the last kid. Charter school the next year and it was everything I'd hoped it could be.