But that's more of a feature request, or even a completely different product ("I would like to send SMS from my desktop"), than a design decision for a chat application's protocol.

Sure it's a feature request but a feature that would be much simpler if the messages were routed through the phone any way.

Your message history is always synchronised between devices, it doesn't sound like rocket science to make the client detect when a message is meant to be sent as SMS. No need to make the design choice of routing all traffic through the phone for that.