Fair enough. Models tend to be imperfect, and music theory is definitely no exception to that rule, and we attempt to model music because we care about the underlying phenomenon (music).
As someone who enjoys listening to music, creating music, and music theory, I'd characterize the latter as providing a specialized vocabulary; an approach to listening, since words in the vocabulary represent concepts that you can hear; and a toolbox of concepts you can draw from.
It's a model, you can use it as much or as little as you like. And there's more than one model, and sometimes the different models overlap more or less, and you can choose any of them or none of them and still make and enjoy music.
The other thing it provides is a wildly complex logical system with fascinating philosophical connections. Some people enjoy exploring that more than making music with it, and that's also okay. I've certainly gotten a lot of enjoyment out of that. It's made me a better thinker. In math, formulas can be elegant. In music theory, different constructions induce different experiences.