See the last sentence of my comment: it's not consistent with experiments. The success of quantum mechanics as a predictive tool comes from acting as if the wavefunction is always present, no matter what aspect of it is measured.
There may be a whole different theory of physics which can replace quantum mechanics and doesn't have wavefunctions, and has completely different simulation requirements, but at that point you could postulate anything.
There may be a whole different theory of physics which can replace quantum mechanics and doesn't have wavefunctions, and has completely different simulation requirements, but at that point you could postulate anything.