I too have a pair of very light non-breathable chaps. Not only are they very lightweight, they're also very low bulk, so I'm happy to toss them in if a trip looks a bit iffy.
It's not about staying dry, it's about temperature control on colder trips. In that context, breathability isn't important. Indeed, they can breathe a little better out of the tops than do rain pants, but those tops are typically covered with whatever rain jacket or poncho you're wearing, so ---
For me, chaps are something to wear if I'm *cold*, not just wet. I mostly carry them for insurance on some trips and rarely wear 'em.
One issue I find is that if I have on the chaps, I don't want to take off the jacket/poncho without also taking off the chaps right away if on a populated trail, because if you walk along in chaps and no jacket, folks look at you like you're a bit of a perv ... :-)