There are plenty of better ways. You make the student auth in some manner then grant an exception from your own computer.
Entering the password on the student’s BYOD is pretty stupid
Entering the password on the student’s BYOD is pretty stupid
I wouldn't say it was stupid of the teacher to enter the password, given the amount of technical expertise that elementary school teachers can be expected to possess.
The blame should probably go to the person who set up the exception-granting system, who should have used a system that doesn't involve authenticating on a non-trusted device.