So, I am missing something, how does it work with the double slit experiment ? the result should never act as a wave without observation if we have spontaneous collapse all the time ? Or is this spontaneous collapse quite rare in practice ?
The nice thing about spontaneous collapse is that it makes a testable prediction: there should be a scale at which the behavior of an isolated system starts to show divergence from quantum predictions. So far that prediction has failed to be demonstrated, but people are still working on it.
It's extremely rare for a simple quantum system like a single electron; but it is happening basically all the time for a very large system like the detector in the double slit experiment. So basically, the electron is virtually certain to get all the way through the double slit experiment without any spontaneous collapse, but as soon as it interacts with the detector screen at the end of the experiment it will have to collapse basically immediately, because the detector screen is always having spontaneous collapse events and the electron is now entangled with the screen and has to collapse along with it.