Huh, I'd never realized the connection between PoC and LCPW before. I'll have to think about that, although I wouldn't necessarily say LCPW is a replacement for PoC. They solve different problems in practice--like lessdazed said, PoC can be more effective at countering overconfidence in knowing what you think your opponent meant, if that's the goal. Would you mind giving an example though?

ETA:

For example, you search harder for possible reasonable interpretations, to make sure they are available for consideration, but retain expected bad interpretations in the distribution of possible intended meanings.

I agree that if you're going to use PoC, you shouldn't apply it internally and unilaterally--if responding as though your opponent made a good argument requires some unlikely assumptions, you should still be well aware of that.