Many schools may be building (or having built) Android and IOS apps for their schools. With some work on BBK-12 part the ability to have a PWA that could be pinned to home screens and offer notifications could be made available to all schools.
Microsoft - https://docs.microsoft.com/en-us/microsoft-edge/progressive-web-apps
Google - https://developers.google.com/web/progressive-web-apps/
Apple - Improving through the IOS 12.x lifecycle
If this feature set was built into the core web service it would enable it for all schools.
Yes! This would be great. We attempted to teach our parents how to bookmark the website on their phone so it looks like an app.