As it stands right now it almost never makes sense for Prince to stand as king. Odd considering that completely contradicts the royal hierarchy. So how about a new passive for the Prince.
Heir to the Throne: Prince receives all abilities of a starting king when stepping up to the throne. (i.e. all stacks of "allies)
If that seems too strong (could be in end game) could do this instead:
Prince receives 2 additional uses of “allies” on top of what the previous king had, up to a maximum of 4.
Now BD has the option to vote in someone for extra investigates at the cost of losing the Prince. Prince stepping up becomes a strategic decision rather than an auto lose.