Surely the 'solving' part of CSPs may be obscure, but the basic concept can be readily explained with the metaphor of crosswords and sudoku (both are very direct instances of CSPs); there's not much obscurity to that. In fact, the article resorts to that same metaphor to explain with precision what the 'waveform' metaphor couldn't.

Of course terminology for CSPs will get confusing when you get to represent them mathematically; but that happens to anything that you turn into math. The core concept is quite familiar and intuitive.