It is not realistic to expect that this information is practically accessible enough for it to be immediately provided to EMT services in case of a health emergency, or for it to be of much use if it it was. By reading the posts here, you’d think California and other states which do not require this information were endangering their student/athletes, and all states were endangering their non-athlete students.
It seems that some posters are going to great lengths to make excuses for extremely invasive policies with little legitimate value but fraught with potential for abuse.