I don't think I would call this a "measurement". A measurement, in the Copenhagen interpretation, is a fundamentally non-unitary process. What you're describin

I don't think I would call this a "measurement". A measurement, in the Copenhagen interpretation, is a fundamentally non-unitary process. What you're describing is simply tracing out the environment, so that we end up with a mixed state. The complete density matrix, however, is still being governed by the Von-Neumann equation and therefore evolving unitarily. So I assume what you're saying is that we don't need to model measurements separately since their results would be described by statistical ensembles and, at the level of a subsystem, you can't really tell the difference between a genuinely entangled state and a statistical ensemble, anyway?