Schools will never teach kids their rights to any useful or applicable extent because schools routinely operate in the gray area at the limits and creating a bunch of students who'll call them out on it would make their jobs harder. Same reason they don't do much to teach critical thinking.

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 am of the opinion that "lockdown" is illegal detention, and conditioning them from a very young age to accept it.

The malcom in the middle episode about the ACLU or Rock and roll high school are classic examples of this.