This is just a theory but...
What if the reason why Il became the king instead of Yuhon was actually because Soowon would be unfit to inherit the throne next?
If Yuhon became the king, and took Yonhi as his wife (which he did), then their offspring and any future heirs would be doomed to a short lifespan.
Maybe, Yuhon intentionally choose to give up the throne to marry Yonhi...?
This might also explain why King Il was so against Yona marrying Soowon, assuming Il knew that Soowon had inherited his mother’s condition.