In the waterfall model, wireframes indeed make a lot of sense insofar as they make the user experience tangible and can be handed to developers. They also considerably reduce ambiguity.
Yet wireframes makes less and less sense in the current context. First, executives have become more and more used to gorgeous user interfaces, and no one would argue that wireframes are meant to be awe-inspiring. While wireframes are indeed better than text-only functional specifications, the user experience they procure is definitely worse than a fully functional prototype. As Stephen puts it, "how can we possibly expect to get good feedback on such an incomplete experience?"
It is pretty clear also that the waterfall model does not keep up with an ever-changing world. This model makes sense in a highly-deterministic world, where nobody changes his mind and everybody is able to make decision quickly. In reality, we've all experienced clients changing their mind in the last iteration. There are many reason why this happens but according to Stephen the main one is indeed that "human beings don't think about content separate from presentation separate from structure separate from [fill in the blank]…":
Asking someone to comment just on the interaction or just on the structure--independent of the other pieces -- is a bit like asking someone to judge a chocolate chip cookie based on only a handful of ingredients. "Here, these are the wet ingredients (eggs, sugars, vanilla)--what do you think of this cookie?"
I think that prototyping will replace the waterfall model. It provides numerous advantages:
Check out also this great presentation by the Handcraft folks: Focus on the details rather than skipping over them.