There's nothing arrogant about it. Unless there is some massive, mindblowing change in Stannis character, which would need a lot of page time to establish in the next book, then it's fucked. The show certainly did not do any job establishing a plot that convincingly let it happen, and this was GRRM's idea supposedly. I'm supposed to feel any confidence that he's going to get it right in the books if he goes down that road?
Sure it can happen, and if he does a decent job of it I'll say so. But there's nothing arrogant about it. Unless there is some massive ground shift in the character in the next book, it's all wrong.
Again
We're talking about the same Stannis
The same Stannis who burnt his clansmen to empower his sword
The same Stannis who locked his daughter away with books because of her looks(And only started showing her after Melisandre convinced him)
The same Stannis who, despite his straight character, cheated on his wife and fucked melisandre to create a demon to kill his baby brother
The same Stannis who doesn't believe in punishment, only in burning those who does what he thinks are bad things
This very same Stannis wouldnt' burn his daughter if he thought it would get him the throne? This very same Stannis who thinks he's the foretold warrior of light chosen? The very same who's already committed filial murder?
Stannis has been off his rocker for a long time now.
Consider on top of all the groundwork the book lays down to let us know he'd never do that to Shireen, he doesn't even NEED her in the books. He has access to other people with Kings blood. Tell me, exactly why would he burn his own next in line when he has Theon?
You're right, he doesn't need her. She's baggage to him, so him killing her ot advance himself...isn't that farfetched. And Theon doesn't have kings blood as ascribed by Melisandre, after all their 'claim' to that type of kingship was revoked long before after losing. If anything, the Ironborn are pretenders to the throne, not of real kingsblood.
(In fact, Stannish showed more love to Shireen in the show then in the book.)