The reason I think it's important to understand measurements as models is this: I think there are certain phenomena that the current state of sound science fails to explain. I think that sound science is consistent-- it's a set of observations and theories that reinforce each other. I think it has holes, however.
But first I'm finding it hard to believe that anyone would think FR is not a model. I'm interested in the reality of how it is used and measured. Apart from that, it's just meaningless numbers.
However, I think that I've been a little too rigid about defining "models" and indicating how they are used. I admit there are a lot of ways that models are used and defined, but this doesn't change my point about FR.
I would be interested in how people here would answer the question: "Why do we measure FR?"
Besides that I'll note that FR models a device as linear and can be used to predict its response to future signals that have not been previously measured, although not with perfect accuracy.
Which phenomena are the ones that aren't explained? Where do the holes show up? How do you know there are holes? Can you demonstrate or elaborate on them? If you're talking about unexplained perceptual phenomena then many of these things claimed are unproven. It is impossible to know with 100% certainty whether they are real in the sense that many people think they are (some difference in sound output causes a perceptually different response) or just a product of psychological biases and other nuisance factors. Until the former is proved we tend to think the latter is more likely in many cases. When you furthermore talk about perceptual accuracy, this is a moving target and varies from person to person.
The Fourier transform or the measurements may or may not be models (okay, we can call them models if you want). If we claim a certain device has a certain frequency response then implicitly we have characterized its performance with a model, yes, which has known limitations for accuracy. We measure FR because for many systems it provides good predictions of systems behavior with a range of untested inputs. Anyway, that is why, if necessary, additional and more accurate models are used.