As you have spotted there is an approximation involved in the theory. Almost every physical theory will involve some kind of approximation and/or is designed to only cover a restricted range of parameters. Many theories have no means of getting a useful form of solution (like a formula) and need numerical simulations to produce practical results.

The mathematics of a more detailed analysis of this problem would be a significant burden for high-school students and even first or second year undergraduate students, who would also be getting more advanced mathematical training as they studied physics.

The important issue is what the experiment shows - the wave behavior of light. The basic theory is "good enough" for this purpose. There are much more advanced versions of this experiment which are used in demonstrating aspects of quantum theory and these, unsurprisingly, require more advanced theories underpinning them.