In India I had to give a photocopy of my passport, my permanent address in India, and a letter of referral from an Indian citizen to get my Airtel sim card. It was one of the weirdest experiences I've had in the country.

I guess that's only for lost SIM cards?

I've got my number transferred to new SIM card, about 30 times over last 10 years, without any police report. Had to produce ID proof which is quite convenient.

In those cases you would have the physical possession of the old SIM, so I guess no one can just claim to be you.

Example form for others reading till here - https://discover.vodafone.in/documents/pdfs/simreplacement/s...