What you are saying is that whenever we, the observer, leave the QM model we use the collapse as a computational trapdoor function? Sounds like an interesting point of view.
But would that not also imply that we should be able to measure the quantum world with quantum devices? Say we have a quantum property that is extremely close to p=0.5. If we could invent a device to replicate that property perfectly and measure it repetitively we could then estimate ever more accurate boundaries for the "true" value of p, no?
That's why the wave function "collapses": Because it collides with the non-quantum target.
It's a useful approximation, but of course in reality, there is no such thing as a non-quantum thing.
And if you evolve the target's wave function with the wave function of the particle, then there is no stochastic collapse.