Or perhaps more precisely: "There is no wave function. The wave-function we talk about is just a mathematical recipe for computing the expected test-observations".
Functions are abstract things, they don't exist in the physical world. They only describe the physical world, at best.
So that really leaves the question why do our measurement results follow the predictions of the wave-function unanswered. I think we would like to come up with some theory of why the wave-function so closely predicts our observations.