Is there anything stopping the crownholder taking the King card every turn?
Getting the crown is usually a small reward in comparison to, say, the architect or the thief abilities. The only way this can be a good strategy is focusing on golden districts. At that point, is it easy to target the king with either the thief or the assasin and break the advantage of having the crown AND a useful ability.

In short, there is no way of stopping some player keeping the king forever, but there is also not a good reason to do so.