It seems to me that switching SIMs provides little privacy benefit, because carriers, data brokers, and the adversaries of privacy-desiring people whom they share data with are obviously able to correlate IMEIs (phones) with IMSIs (SIMs).
What kind of specific privacy threats do you think are mitigated by using different SIMs in the same phone (especially the common practice of using an "anonymous" SIM in a phone where you've previously used a SIM linked to your name)?