Schools aren't really subject to the Fourth Amendment and students explicitly have lesser constitutional rights, so they don't really need to worry about gray areas or limits.

The main problem with the suggestion is rather that

1. Schools typically do teach students about their Fourth (among other) Amendment rights, usually in a high-school civics class at the very latest, many students just aren't particularly interested or don't particularly care about paying attention in class.

2. Every time there's a skill or pool of knowledge many adults don't have we default to "They should really teach this in school instead of all the other stupid bullshit they waste their time on," but it turns out all the stupid bullshit they waste their time on is other skills or knowledge pools that people have, over the years, agreed that they should really teach in school. So either you're proposing that schools get more funding and students are kept there for more hours to teach all the additional skills you want students to come out with, or you need to choose a subject to cut, and rest assured that any particular subject you choose will have an existing group of advocates leap to its defense - if it didn't, it would have already been cut after Reaganomics, NCLB, the 2008 GFC, COVID19, or the numerous other occasions we've found opportunities to trim school budgets.

I don't know when you went to high school, but my entire district cut their civics course for being "irrelevant to the educational goals of the district".

I was part of a group of students that did post-school discussions off-campus of civics with those interested, often discussing how it has become harder and harder for students to retain their rights in the public education system.