I found myself a couple of time discarding the King so my opponent wouldn't have the chance to pick it and taking the crown from me. It kinda felt overpowered, but probably there's something I'm missing...
Possibly. In a 2p game one card is discarded face down at random. The first player picks a card then hands the remaining 6 cards to the 2nd player. The second player chooses one and discards one, the first player chooses one and discards one and finally the 2nd player chooses one and discards one.
So the first player can't chose to discard the king face down until they are choosing their second character. The second player can discard the king face down but if they do the first player will keep the crown.