I'm trying to say that if it is cheaper to let climate change happen, because externalities are determined to be $X and taxed away, but people value energy more, then climate change will happen. Which is bad if one doesn't want it to happen.

My conclusion, then, is it may be bad to talk about externalities. At least as economics jargon, and it's confusing to use it otherwise.

It's a tool that isn't bound to doing what people want it to do.