Henri Poincare explained it in his famous 1902 book:
The object of mathematical theories is not to reveal to us the real nature of things; that would be an unreasonable claim. Their only object is to co-ordinate the physical laws with which physical experiment makes us acquainted, the enunciation of which, without the aid of mathematics, we should be unable to effect. Whether the ether exists or not matters little — let us leave that to the metaphysicians; what is essential for us is, that everything happens as if it existed, and that this hypothesis is found to be suitable for the explanation of phenomena. After all, have we any other reason for believing in the existence of material objects? That, too, is only a convenient hypothesis; only, it will never cease to be so, while some day, no doubt, the ether will be thrown aside as useless. [Science and Hypothesis, chap. 12, 1st paragraph]Yes, I could not say it better today. The object of mathematical theories is to make sense of quantified experiments, not to be a perfect description of the real nature of electrons.
The aether is a convenient hypothesis, because our best theories assume a pervasive and uniform quantum field. Even in a vacuum, it has energy, Lorentz symmetries, gauge fields, and virtual particles. Quantum electrodynamics is all about perturbations to that quantum vacuum. In the early XXc the aether was cast aside as useless but it keeps coming back under different names.
It is foolish to think that the true nature of the electron is its wave function. That is just a mathematical device for predicting observables. Attempts to clarify the nature of electrons with hidden variables, as by Bell and his followers, are even more foolish.