As a parent with kids at three different schools, help keeping track of their schedules would be amazing.
Currently updates from the schools are spread over multiple sources: paper notes, email, sms, "news" and "calendar" in school app (which are not kept in sync), and Facebook. Different schools use different apps.
Additionally the channels are often noisy, with messages about groups my kids don't belong to, and "helpful tips" like how to pack healthy lunchboxes. These notifications come in during the day while I'm working, get dismissed due to the low SNR and then the useful ones often slip through unnoticed.
Definitely an area that is ripe for disruption, but as others here have commented, I don't feel confident about Google being the provider.