`If I were a student, I'd be terrified. I didn't cheat, but I could still be accused of cheating for having a solution "too similar" to some other solution. Saying I've waived my right to defend myself against accusation because I didn't admit to something I didn't do would drive me crazy. I'd have to lie about cheating just to avoid the more severe punishment, despite not actually doing the behaviour the administration wishes to discourage.
The fear of punishment that's unconnected to misbehaviour will drive lab rats into neurotic self-harm, and students are pretty similar to lab rats.