You can’t remain unlinked to your real identity as seen by the government because you need to provide your id when buying a new SIM

This varies by country. In the US you can buy a prepaid mobile phone with cash and supply it with prepaid cards, all without showing ID:
https://en.wikipedia.org/wiki/Prepaid_mobile_phone#Privacy_rights

(but obviously they can figure out who you are by tracking your signal and seeing where you spend your time.)