"Long story short, too late" in terms of plot devices and writing. Without the conflict between the houses Atreides and Harkonnen with imperial Corrino hovering (not to mention the BG), the realization of Paul as the quickening of the way would not exist as such; the Fremen were already keen to take his water without question. House Atreides would mean nothing to Arrakis without their prophet come to dwell among them, and Arrakis would mean little more to the Atreides of it or its people if they didn't need any winning over, let alone have a Missionaria Protective prophecy (and religion made law) built in to their own reasons for survival as Fremen.
Shaddam (or other forces) set himself up to fail in the imperium by imposing rule on the desert planet. He avoids nothing in sending his cousins to die; he thinks he is ten feet tall and bullet proof.
The Fremen didn't blink when the Planetologist told them it would take generations numbered beyond understanding. Not unlike the loyalty that the Atreides command and earn. '"Sire!" and the word was torn from him' (paraphrase, citation to follow).
Without the possibilities of survival that Leto names (taking over the duty and ethics -- desert power -- or going rogue with the house atomics) and the possibilities the Bene Gesserit have in mind (ibid and a kwisatz haderach), Paul would have been as spoiled a crown as his Harkonnen cousins and Irulan. They didn't win any fans on Arrakis, but Leto saw injustice off the bat and changed the Harkonnen waste water customs. Would Leto or Paul have done the same if the planet were handed to him with Irulan's hand?
Fortunately the BG didn't give Shaddam IV any sons, a quick twist on genetics and the control of every cell of the body.
Irulan and Paul are about the same age (Paul is a teenager, y'all, it's a coming of age story too) and she does speak of her father's wish. For her to marry Leto, nothing but customary politics seems to forbid it, and to Shaddam and the length in generations, it can be only a dream of his within the scheme of his, the motivation for which he does not fully understand, heavily if not fully influenced by the BG breeding program. Let's not forget they got there first.
In the trifold of power existant at the beginning of the first novel, Shaddam is more like a lone Bishop, or the Emperor ever married to the Queen. Of course, the emperor is not the only one who thinks he is the master manipulator on the ivory keys.
You cite the wishes of nature vs. nurture. Irulan is a product of her raising who in her books and actions defines it, defies it, and realizes it.
Her counter to Chani is an emotional and plot breaking point for all of them. If Shaddam had married her to Leto or had arranged her engagement to Paul (the Emperor wouldn't dare have his daughter be a concubine or reveal her strength as she was BG trained like the poor Lady Jessica) to begin with, there would be a thousand different "what if" paths to the kwisatz haderach landing on the planet with the greatest hydraulic despotism in the universe.
Story over in five pages when the Wizard grants Dorothy her wish before she ever meets her friends, tins, foils, or foes, and no one looks behind the curtain. Then Dorothy would have no allies, and she did not defeat the fastest broom in the West by herself. There was at least one small yappy type dog involved.
