This sounds like the SIM-dance I do when I travel. The carrier I use (Google Fi) because it is the most cost-effective/convenient that I can find for nearly constant international travel has an important limitation:

From the time the SIM leaves the US, it gives 90 continuous days of international use and then craps out until it touches the US again (at which point it awakes). So, that means I calibrate the most important 90 day stretch of a trip outside the US, remove the SIM from my phone when I leave the States , reinserting it at the beginning of my desired window, at which point it works for three months. I use local SIM chips for the balance of the trip.

Obtaining these can be a paperwork nightmare (like in India) or as easy as buying them, without providing ID, over the counter from a kiosk, in places like Indonesia. Even those which support international roaming are available for a few bucks.

If you used one in the States, especially with an unlocked phone picked up second hand in a street market, while it would stick out as foreign phone it would certainly obscure its owner.

Jeff