I have read your post; you are still incorrect. Here is what you said (in bold):

Consider, for example, the case where the C4 app is used to turn the fireplace on.

OK, fully considered.

Now, you want to use the physical switch to turn it off. Guess what? The physical switch is already off. (The work around is to flip the switch on and then back off, but this is not exactly user friendly.)

This is where you are incorrect.

If I start the FP from elsewhere (not the mechanical switch).
I now have the FP on.
If the mechanical switch is in the down position, press the top position.
FP goes out.

If I start the FP from elsewhere (not the mechanical switch).
I now have the FP on.
If the mechanical switch is in the up position, press the down position.
FP goes out.

Try it out.