Yes they do? You can install system wide Tor on android. If you are referring to the fact that phones emit signals that can be triangulated, that doesn't interfere with anonymity in and of itself.

The fact that towers can ID which phones go where does interfere however.

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.

You could use the same argument for the radios in your home and WiFi. And anonymity is about your name. If they can locate your phone but not be used to identify you then it doesn't break anonymity.