Punishing honest students by ensuring that they will fail unless they cheat is an absurd solution. In school I went to great lengths to do my work well and on my own. It was disheartening to see other students openly cheat and do well, but at least I knew that I was performing well on my own merits.
Under your system, I would have been actively punished for not cheating. What's the point of developing a cure that's worse than the disease?