I mean Soo-Won's motivations are a little bit forced, but I can understand - from an internal logic sort of standpoint - why he needed to kill the previous king.
It's revenge.
I don't even know if the king actually killed his father or if he's just been led to believe that. But his whole thing is to be a strong king and therefore, he had to "kill" all the weaknesses and let go of the two friends who are/could become weaknesses.
Soo-Won isn't trying to be a morally better king, he wants to be powerful enough to unite the tribes against a common enemy. He has no standards, he's made that abundantly clear. He's desperate to make the country strong for whatever reason.
The easier, obvious solution was to marry Yona, of course, I think we all agree on that. And King Il's objections aside, there's ways around that without bloodshed.
But in his own, twisted logic, this easy way isn't the right way. He's doing all this for the "greater good".