First. The declaration was made LONG ago, at least 10 years. It's not Soma who had to sign it, but the previous king.
Second. "There's a trap in the declaration". Wasn't Soma trying to "teach" the princess or something? But now we're not told what the trap is simply to leave a cliffhanger. I mean, I still think the manga and mangaka are better than average, but...eh.
And yeah, as everyone's saying, something's hella backwards with that idealist/realist definition. Might be the TL, might be the mangaka, might be the LN/WN author. At this point it's hard to grasp...