this is a reasonable way to understand the nature of the wavefunction, especially for operators with continuous spectra. it s not clear to me that this squeeze notion can be used for operators with discrete spectra, like spin. in any event, physically reasonable or not, this is not the orthodox position of QM. the axioms of quantum mechanics describe a complete collapse of the wave function, after an ideal measurement. there are a lot of people who don t believe in the complete collapse of the wavefunction, like these many-worlds interpretation people. if you want to propose a looser interpretation than the orthodox one, it would be nice if you could come up with a sety of axioms, but i don t imagine that sort of thing is too easy... in any event, the point is that the orthodox position with it s wavefunction collapse is sometimes a bit hard to interpret.