And no one in the room thought, hey, only three people in the room want this, how about we just hail caesar them? I mean jesus christ, serving the crown sure, but if it means there wont be a crown by the end of the day then what's the fucking point.
You have to understand kings back then were deity.
Sure, the core supporters of the first prince would be willing to commit regicide, but most of the other factions will not and will even condemn such action. It would spark a civil war. And given there's an enemy army nearby, they can't afford it.
And even if they could it would cast a shadow over the legimity of the first prince as king.
It would also be ground for every other nation to form a coalition army against zhao.
Ryifui's plot nearly worked because he cultivated links for decades and engineered a decent front. He would be saving the nation not taking down the rightful ruler.
Assassination would work, but not a frontal fight