You can make and receive calls with the phone off or in AirPlane mode. I commonly ditch my phone in the trunk of my car when I'm going for a run and I still get calls and although not SMS I can still receive iMessage notifications which is fine for me because most of my personal network uses iOS.
I don't have any specific implementation details about SMS to explain why, but one could surmise that there is some limiting factor in SMS that means that it can only be targeted directly at one cellular device and although the watch soft SIM takes on the number it's actually a separate line. Also, the notes from my carrier (EE) say that to receive SMS the phone needs to be on so it may well be that the watch can continue to send SMS but not receive them (I haven't tried this).
I do know that when I leave my phone at home and switched on, when I run from there, I get the full range of other notifications from all apps popping up including SMS.