You asked “How can it be that a model that does not describe reality in a faithful manner can help us explain real world phenomena? ”
Have you ever seen a stage magician in action?
Consider that it seems probable that all of our perceptions, what we think of as reality, is really only a subconsciously assembled model of reality, consisting of the distinctions and abstractions available to our neural networks due to conditioning by past experience.
What we think of as experiential reality, seems to be a model, and it does seem to have a certain set of utilities (though not so many around stage magicians) 😉