The repetition, the directness, the absence of irony or critical apparatus — these are the things that move Charlie. He believes the essay is more honest than anything Ellie will write as an adult once she has learned how to perform the appearance of analysis. He believes honesty is the thing that is hardest to sustain.
Samuel D. Hunter wrote The Whale as a meditation on the life of his own father, who struggled with obesity, and on the experience of growing up in Idaho with a complex relationship to evangelical Christianity. The essay within the play is not simply a plot device; it is the play’s argument about what writing is and what honesty costs.
For the film to carry this argument, the actor playing Charlie had to make the essay’s importance to Charlie legible — had to make the audience understand why a man who is dying is spending his last days fixated on something a teenage girl wrote about Moby-Dick. Fraser accomplished this by making the fixation feel specific and true rather than symbolic or contrived. The essay is important to Charlie for the reasons the film gives; the performance has to make you believe those reasons.
The reason is: the essay tells the truth in the way that Ellie no longer tells the truth, and Charlie is afraid that he has contributed to the loss of that truth-telling capacity by being absent from her life when she needed a father. The essay is evidence of who she was before he failed her. He is trying to reach that person again.