Elementary School - Private or state? Does it matter at this level where you send your kid?

We live in a mid-sized university town in the midwest. While some parents send their kids to Montessori or a religious school, the vast majority send their kids to the local public schools. We did the latter, and my kids turned out perfect! Well, that’s just a hyperbolic figure of speech. But my point is that if you have high quality public schools (and in our case also within walking distance from home), there is no harm at all in sending your kids to the same ones that most of their neighborhood kids are going to. My kids ended up attending “elite” colleges. But they’d have done well attending our public universities. My kids grew up with a lot of interesting and talented friends who they also interacted with in local sports, music, and art activities. And some of these are lifelong friends with whom they remain in touch even well after college, and even though they may live at opposite ends of the country.