We don't put first aid kits in every room because they don't really use it and the clinic is accessible. Some teachers would ask for band aids for students who will complain of microscopic boo boos.
Frankly regardless of the case I would prefer to see it myself than let the teachers intervene.
We provide first aid kits for our school bus (they are also trained to do first aid every beginning of the school year). It contains 2 pairs of gloves, brown paper bag, sanitary pad, plastic, band aids, 2x2 and 4x4 Sterile gauze, betadine, spirit of ammonia, micropore tape, cotton buds, cotton balls, kelly forcep, bandage scissors, elastic bandage 2 " 3" 4", ziplock, thermometer, alcohol, and contact numbers.