Ducal families weren't the sort of thing you pissed off willy-nilly even if you were a ruling King you know. Those guys were right below the monarchs on the aristocratic totem pole and more to the point before modern centralised states were more often than not practically minor kings themselves in all but name, who could go to open war against their nominal suzerain and win.
Shit - at least one (William the Bastard of Normandy, better known as "the Conqueror") went and conquered himself a whole kingdom on the side which resulted in some pretty complicated feudal relations down the road.
Which would be the "lolpolitics" I referred to earlier. By the sounds of it this match was arranged between the King and the Purpleices for strategic reasons and both oughta have a decent bit of political capital riding on it. The Heir Apparent publicly outing himself as a complete tool isn't particularly going to change the calculus, as his questionable intellect would be an open secret in the court anyway.
You might also note that on the same page Shelphie sighs and mutters about the Maid's "optimism" rather implying it's not nearly as simple as she claims. Something similar can be inferred from the fact that the Prince seems to find it necessary to level fairly serious charges (practically amounting to attempted homicide) against Shelphie in his harebrained gambit to get the engagement annulled implying he can't just nix it without serious leverage either.
