Interesting dilemma. His alibi is that he's too weak to ever do this to the prince. Killing him technically is airtight, but he loses favor with the princess and potentially if found out later is 100% fucked. On the other hand, letting the prince go means it's a question of whether the prince's pride will bury the incident or whether the prince will try to get revenge. From my understanding, it's better to let him live, because if he keeps the brace, he can beat the prince again whenever he wants, which means he doesn't have to deal with the looming possibility that investigation into the prince's death can fuck him over. His alibi would be the same then, but less airtight, but the prince also wouldn't be able to just openly attack him - so it would be a similar situation to now if he ever were to get back at MC in the future, in which case it still checks out. In the end, it's best to let the prince live because it garners favor with the princess, avoids some really terrible outcomes in a worst case scenario, and still puts him at no more a disadvantageous position than he is in right now. I want to see the prince die, but it just makes sense to let him live. It's not easy to cover up the death of a royal. Feed them all to the monsters, whatever, it's a world of magic. If someone could talk to spirits, it wouldn't end well for MC.