“Similarly, I can well imagine that the student’s desire for the monetary reward will find other channels of expression than studying.”
You mean they are actually studying today???
By that logic, employers shouldn’t pay people for working because they’ll probably cheat, anyway. Everyone will just voluntarily work for no pay because they’ll just want to “do the right thing” for society.
Well, look at private schools, or colleges. Parents and students, often via loans, pay for the privilege of this instruction. Should the parent pay the child for submitting to the instruction purchased at great expense? Or should the student pay himself for attending college?
If school is so onerous a duty that it requires compensation, why not just dispense with it? Let the children break coal, and be useful.