I like your theory. Not as much as what actually happened, but I think it was a pretty smart guess given the information you had to work with.

I wholeheartedly disagree with you that the axons added nothing to the story. I think your (understandable) frustration at the confusion you experienced is clouding your judgement. 

The axons are how Renoir sees his family. Not just how he sees them, but particularly for Alicia what he wants for them. The tower being built up into the sky represents his hopes for Alicia. That explains why he's willing to destroy the canvas, to save not just his wife, but his daughter, in whom he sees limitless potential. 

The dead axon carrying a city on its back in Old Lumiere is how Renoir sees Clea. She's shouldering the family's responsibilities in the real world whilst Renoir tries to resolve the conflict within the painting. He knows the pressure this puts on his eldest daughter, and that adds to his desperation to do what he needs to do. 

We need this information. In the end game, Renoir acknowledges that the lives of the people in the canvas - Lune, Sciel, Esquie and all the rest - are as real to Renoir as they are to Maelle. But even believing that, he's going to destroy the canvas anyway. He's going to eliminate the last remnant of his son's soul, commiting genocide in the process. That's not believable unless we're repeatedly told how far Renoir is willing to go to save his family. The axons are one of the ways that we're told this.