Uh, does it really need a detailed explanation? You know human mind is quite complex.
They are royalty, the person in power.
What will people say if they leaked the fact that the princess is actually a nonexistent person?
Mind that she generates a body that basically not different with normal human in the other people's eyes.
It will create unnecessary turmoil in the kingdom.
Okay, why don't they tell the prince before she contributed anything? It should have taken a lot of time before those contribution and amass assets (like years) so they have a lot of time to tell the prince before they become uncomfortable in revealing it. Not to mention, they could just stop her. They are the King and Queen and they are the parents. Seriously, you are trying to make the King and Queen stupid just for the sake of the plot.
Okay, another logical fall through here. The King and Queen is supposed to be ignoring her, now they send her to a Magic Academy . . . Why? They could just, I don't know, keep here in the castle?
And why they need to stop the princess? She creates the solution for their problems. Food shortage, economy crisis, etc...
Then, if you are about 5-12, and you have a twin sister, but your parent tell you that "your sister is actually not exists, it's just your imagination".
And there, you see your sister outside the window, training swords with the guards/instructors. Then what will you think?
Perhaps they will tell him (and her) after he becomes adult, but they were already too late by then.
About sending her to magic academy, she is talented, prodigy, and stuff... How could they keep her confined?
It will only arouse suspicion by their vessels if they do so.
Also what will happen to the prince if they were separated far away, no one knows as well and they also didn't dare to take risks.
And as I typed in previous post, they are unaware of the threat. Basically, if she didn't use much magic, then all is fine.
But if she used magic in daily basis, you can't help but notice something is wrong.
And why wouldn't they feel her as a threat? She is abnormal and has something to do with their child (most likely the heir). There are actually a strong reason that they should fear her.
The girl is a cheerful, kind girl, cared for her brother very much, contributed to kingdom development, etc... etc...
Oh well, any reason can be made.
But basically, she shows 0 threat to their life. On the contrary, she brings prosperity and wealth.
Even if they do feel uneasy, they also can't let go this kind of existence too, don't they?
And why are the King and Queen not do anything? I mean, they suspected something, then why are they letting them be unsupervised or something? Heck, the prince should be confined to his sick bed, because he is sick, and the girl imprisoned or something after their discovery so she wouldn't do anything to bring further harm.
The prince should also aware that incest is wrong, so he definitely won't do things openly. He wasn't brainless either.
It's just because of the plot that it got revealed. That's all.
About the sickness, as I said earlier, the symptoms are just simple tiredness. He did not immediately coughed blood or something.
It didn't alarm anyone enough to confine the prince into the bed, until few years later.
And, after the discovery... Well, that's the conflict lies. Let's leave the author to do the narration.
Not to mention, how old are they? They should be too young don't you think?
Let's just say, they're 18 when the incest/selfcest? take place. Minimal age for adult content in this website.
Seriously, I don't know why I need to type all of this... It's just a prompt.
This should be left to the author's imagination to fill the loophole if he or she wants to use this idea.