I'm not trying to be snarky or anything, I'm genuinely curious here what the benefit is to you.
Guess what a SIM card does when it's put into a new phone? Includes the last IMSI it was installed into when it joins the carrier's network.
They're not very well educated on digital privacy and engaging in a lot of cargo-cult privacy stuff that is almost certainly making them stand out like a giant red thumb. Very few people do things like switch SIM cards on a regular basis, at least ones who aren't engaged in criminal enterprises.
Their behavior reminds me of a former partner's ex, who was [paranoid-delusional | obsessed with] cell phone tracking.
I really have no idea why they're so concerned about their cell phone carrier "knowing" their home address.
I think OP might be in a jurisdiction where you don't need to provide your address (yet) when
> using prepaid cash purchased SIMs
If you want to be untraceable you don't use cellphones, simple as that. Of course modern life is ridiculously difficult that way so it's pretty impossible.
I looked into it a little bit, a good option depending on your threat model is to simply leave it in a faraday container (read: aluminum foil envelope - or the more sophisticated stuff) when you don't want it to be visible. But then, you kind of have to let go of having that phone usable at home at all, and end up having a "dirty" and a "clean" phone. Then again, just useful depending on your threat model.
Do you disable cell service manually when you're going home?