Every day, administrators already have to investigate occurrences at school and choose appropriate disciplinary paths forward.
Coursework in legal matters is part of educational leadership/administration programs and is a focus of professional development, in part because districts are incentivized to reduce litigation costs.
I share your apparent concern that districts, etc, screw up discipline often and unjust outcomes occur. However, doing nothing isn't an option, and I don't think punting more of school discipline to the police is likely to improve outcomes.