I'm aware there have been plenty of discussions about Copenhagen interpretation vs ensemble interpretations (myself I have always been more fond of the latter) but I intend to explore new perspectives and stick as much as possible to what QM practitioners do in practice as opposed to obscure metaphysical arguments. It seems to me that when it is argued that the projection operator is always unitary(like in section 9.2 in Ballentine book for instance) unitarity is always(with one exception, that I explain below) assumed at the outset rather than derived by the physics and the mathematical analysis of experiments. The exception refers to experiments that imply measurements with only two mutually orthogonal possible outcomes, best exemplified by the Stern-Gerlach experiment. But in this class of experiments we have a degenerate density matrix that is a multiple of the identity matrix, and there is only 2 possible different eigenvalues, no possible degeneracy of the discrete eigenvalues for the singlet state preparation, so the operator of the observable is also a multiple of the identity, and the projection is orthogonal, no "collapse" here. This kind of experiments are very often used in textbooks as the main example of how QM works in general and it might lead to a limited view of the measurement projection operator when one is not dealing with that special case. I understand why a non-unitary projection postulate might be too hard to swallow as it contradicts the postulates based on the Hilbert space but it appears that the solution of the ensemble interpretation amounts to just ignore individual measurements, something hard to justify in any empirical theory and even more in QM. The postulates of a theory are supposed not be derivable but obtained from experiments, regardless if they are statistical or not. Otherwise one is restricting the validity of the theory to the point that some of the calculations and steps when applied to real problems are totally unjustified. In that sense the(nonunitary) projection postulate is necessary if one wants to give a complete set of postulates from experiments. Not including it would restrict QM to stationary states. For example when doing time-dependent perturbation it is hard to dismiss the individual mesurement used to perform the perturbation as something just magically given, just "given the state". Of course, a situation like this doesn't arise when analysing a Stern-Gerlach experiment, and it is very easy to convince oneself that there is no non-unitary projection using this experiment as an example. I'd say this is related to the special kind of measurement one performs when measuring spin restricted to one axis. But for the more general type of measurement of observables that admit more than 2 eigenvalues, either discrete with degeneracy or continuous, there is a non-orthogonal projection involved, that can only be ignored if one simply assumes unitarity because the formalism says so while in practice getting results in QM often implies using individual measurements as starting point for calculations. Not to mention the ensemble-only view leaves out entropy and irreversibility.