"They run their own OS and can stay on independent of the rest of the hardware consuming very little power."

It's worse - there's a second, independent computer inside your phone that you have no control over: the SIM card.

The SIM is a standalone computer with its own processor and memory which your carrier can communicate with and upload programs to run on it without your knowledge ("OTA updates", etc.)

https://osmocom.org/projects/cellular-infrastructure/wiki/SI...

ftp://www.3gpp.org/tsg_sa/WG3_Security/TSGS3_30_Povoa/Docs/PDF/S3-030534.pdf