In copenhagen you can analyze the interaction between the measurement device and system, you just have to call the device part of the “system”
You can do this arbitrarily and then pretend the collapse occurs at some future later point because “when collapse occurs” is a totally subjective thing of what you define as the measurement
Sure but that's really just a hack. By defining the measurement device to be somehow outside of the entire thing you can analyse another measurement device as if it's not a measurement device, but still it leaves an element of the theory that is physically significant (the new, broader measurement device) that isn't studied by the measurement. This is usually okay, sure, but it means that ultimately my point still stands: Copenhagen can be used to analyse a specific measurement device + system, but whatever measurement device is chosen as the Copenhagen measurement device cannot be analysed by the Copenhagen interpretation in that given example. This is an inescapable problem of the Copenhagen interpretation, and MWI does not have this problem.
yeah i mean i'm very sympathetic to MWI so even my original comment is not going to be very good at defending copenhagen - but i do think the math is pretty much equivalent depending on what you define as the system. just like i could have equivalent math where i was assuming that all reality was actually just God moving around the particles with non-local hidden states only known to Him (i'm not religious though).
You can do this arbitrarily and then pretend the collapse occurs at some future later point because “when collapse occurs” is a totally subjective thing of what you define as the measurement