Well, to explain, the expectation arises out of the fact that POTS handles it just fine. Of course even there admittedly the "beep" tone does technically "blot out" audio in both directions very briefly to your point. But it's extremely brief to the point of almost being unnoticeable.
With the OBI200 at least, the interruption is more significant (no way to time it, but it "feels" like 1-2 seconds) and it's "instead of" a beep. In other words, I'm getting no beep tone despite the settings showing that Call Waiting is enabled and with standard tone selected. Instead it sounds almost like the call-in-progress is temporarily being disconnected.
You could very well be right about the phone hardware as root cause of not seeing the CID - after all it's an analog phone plugged into the OBI200. However, on POTS the CWCID worked fine. But at minimum I was expecting a usual beep tone and not the more intrusive interruption to the call in-progress I'm experiencing.