It’s like Ava said, with Arael, you’re relying on her name and heritage to justify taking over the land. It’s essentially a revival of the Aurelian Empire. Even if you and her change some laws and customs, it would still fundamentally be the same empire, because its legitimacy comes from her being an Empyrean and the daughter of Rahatiel.
If you decide to rule yourself, though, then you’re a conqueror. You can try to argue that it’s for the greater good, for vengeance, for justice, or just because you want to, but regardless of what you call it, even if you name it after the Aurelian Empire or Emberford, it would still be a new kingdom, a new empire.
Gameplay-wise, even though Arael has no desire to rule alone, she would still be the Empress at the end of the day. You’d be able to advise her and sometimes convince her to follow your ideas, but the final decision will always be hers. And if you keep pushing her to go against her own morals and values, it’ll start damaging your relationship with her. And there are some things she simply will never compromise on.
For example, let’s say you wanted to eradicate all worshippers of the Seven Aurelian Gods and make the worship of Azgor the only accepted religion on the continent (just an example, not saying it will or wont happen). If you are the ruler, you can do that. It might destroy relationships and lead to bloodshed on a scale never seen before, but who’s going to stop you? If Arael is Empress, though, she would never allow something like that under any circumstances. Even if the Warden begged her, there are certain things she would never allow. Sometimes you might even know her decisions are going to cause problems, but you chose to put her on the throne, you’ll have to live with that and deal with the consequences.
Ecbert and Theresa’s routes are similar in that regard. Those are paths where you willingly give up part of your control and choose to serve someone else, so many important decisions stop being entirely yours to make.