Most public schools wouldn’t have the budget to allocate a staff member to create and maintain such a distro. It would also take quite some time to flash to all of the devices.

The management tools built into chromeOS are also mature and very compelling to schools. Most schools don’t see the value of reinventing the wheel when a mostly ok solution that takes no extra effort is already available.

The title is fine. The trademark is “App Store”, Not “Apple App Store”.