The IMEI identifies a device. It is, or should be, useful to lock stolen phones, though it can obviously be used to track someone who keeps the same phone even if they change SIM card.

The IMSI identifies the subscriber (and/or the SIM card) even if you change phone.

As long as people are able to call and be called and as long as people need to be billed there has to be a reliable form of identification.

This is not an "intrusive privacy violation", it is, as you point out, a technical requirement of our willingness to be reachable and most people think that the benefits far outweigh the very limited drawbacks.