I think C is absolutely necessary and the game cannot work with it, because this is critical:
> Dropping C entirely would lose the confirmation of 'Seeing both sides'
The game doesn't really work in full ambiguity and uncertainty. Enough people didn't understand it even with C (as you can see if you go read the subreddit about the game).
If it's any consolation, I'm actually deeply worried about this: C is not the salvation we may think. C is not forever, and in fact, it's quite brittle! There's also no, ahem, mechanical way to reverse C back into its... "source". So the source is gone forever; once we have C, C is all there is, for as long as C can last without any failure or decay, which might not be much longer.