Repeatable measurements and the collapse postulate

J. v. Neumann justified the collapse postulate by the empirical fact of the repeatability of a measurement at a single quantum system. However, in his quantum mechanical treatment of the measurement process repeatability emerges without collapse. The entangled state of the measurement device and the measured system after their interaction ensures it already. Furthermore, this state gives the same predictions for the measured system alone as the description demanded by the collapse postulate.