My mother is a teacher. I can guarantee you that she is not in a position to want to or be capable of integrating a student's browser history into her education plan, nor is the school's administration in the habit of doing anything more than looking at standardized test score numbers and random room checks to make sure the teachers aren't beating anyone. Nobody in the school district is thinking "if only we could see what these kids are doing 24 hours a day, we could maybe teach them better". All of this data is being collected for literally no purpose but to get someone in trouble when they do something that could conceivably be construed as "wrong", regardless of how innocuous it is (what are the consequences for, say, watching the DuckTales intro on a school-issued Chromebook? Loss of access? Detention? Suspension?).
Or, y'know, they could provide their research notes and explain their work, like I did when I was in school. Defending oneself from plagiarism accusations is not uniquely possible thanks to constant digital surveillance.
Great. What about households that don't have alternate computing devices, or only have a limited number of them? In your household of 5, if there was only a single family computer, what do you think the chances would be of someone using their Chromebook for something other than school work because their sister was playing Minecraft on the family computer?
Why is that a good thing? It's wildly inappropriate for the school district to mandate that parents allow such a monitoring device into their house, especially if everything is being routed into Google Classroom in the end anyway and can be accessed from literally any device with an internet connection. How are they even enforcing this requirement that students never use anything but the Chromebook they've been issued?