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And not even that.

https://consumer.ftc.gov/consumer-alerts/2019/10/sim-swap-sc...

https://pages.nist.gov/800-63-3/sp800-63b.html

It’s not about the transport medium. My Honda also proxies iMessage and FaceTime.

I don't see how it can do that unless you give it your login details to those apps. And what about other apps, like WhatsApp, LINE, WeChat, or Messenger? I don't know anyone that uses iMessage or FaceTime; I didn't even think those were chat services.

SMS and iMessage are exposed via Bluetooth’s Message Access Profile. Facetime would use the Hands Free Profile. Access to both of those would be requested during pairing of the phone.

At least on iOS, the other apps would need permission to integrate with the necessary API to integrate with MAP. I’m not sure if this is even available with the public APIs.

What else am I supposed to use

The same thing everyone else in the civilized world uses: a chat app like Messenger, WeChat, LINE, or WhatsApp.