Hmmm... I wonder whether he would reveal his secret to anyone at this rate.....

Unfortunately I have to disagree. I bet the moment he tried that, the mother will dispose all the evidences. Even a king can't arrest a powerful family head without any evidence. Also, if he can't prove their evildoing...he's probably going to die...by his family...

Not to mention he didn't reveal this to the princess. He's afraid that the princess may despise him and his family. Knowing that....you think he would reveal to the king?

Technically, a desperate time reveals and amplify human natures. An evil person will become more evil. A kind person will become a kinder person.
With some exception ofc. A good yet calculative push may turn people into a better version of themselves. Like the cook who keeps bribing the baddies his special foods.

He's not crazy. Letting them escape without any plan is crazy and truthfully impossible. Remember, this is just one boy without any power and influence in his household. They're definetely get caught if they walked outside without preparation.
Thus, he end them because he knows that they can't escape from his mother. It's not a really nice ending but I think, it's a logical one.