I mean, it literally interferes with anonymity in the most fundamental way.

"Everywhere you go, even when you're not actively using your phone, it's still listening." - Edward Snowden

With a SIM card, you are by definition always tracked and identified individually. It's how the technology is designed to function. You can remove the SIM card, harden your OS, randomize your Wifi MAC but at that point you aren't really using a _cell phone_ anymore.