In that case, you probably also want to rotate IMEIs, right? I don't know if the feds are routinely considering it, but they could correlate all the SIMs by looking at the unchanging IMEI.
• your wife's lawyer in divorce-court, who would love to compel cell-tower IMEI logs, but has no legal grounds to do so
• your mother who you don't want to be made aware that you're a working as a prostitute
• your abusive partner or parent who you're trying to arrange an exit from
• or, the ever-present cloying example: your friend—who is very nosy and knows your regular phone's unlock code—but who you're trying to arrange a surprise party for
Basically, as a burner phone is to Tor, a side-piece phone is to a browser's Incognito Mode.
Unless people turn off the phone and remove the SIM before switching it should generate highly suspicious network traffic.