If you are required to give them information that they can use to figure out who you are, it’s not anonymous.

So if you are on normal post-paid cell phones, where you have given them your real info, or use a credit to pay for it with your name on it, etc. that means you aren’t anonymous.

So when super secret drug lord is caught, they can figure you were talking to this drug lord and charge you, because they have his end of the communications and can verify with your cell provider who YOU are.

Privacy just means they don’t know what you are saying. They may know you are communicating with drug lord but not what you are saying.

You can have neither, one or the other, or both