Not exactly distilled
Remember the volcanos in Iceland that erupted and basically grounded Europe? If you were downwind any rainwater was most likely acidic and full of fine particles. At any particular time there are numerous spores of fungi, algae, and other microscopic organisms. That's why rainwater is often considered non-potable.
This is not insurmountable. A piece of clean limestone can do wonders to neutralize the acid, and there are numerous ways to get rid of bacteria, etc., in the water. The latter usually involve higher tech than a rock, but the tech doesn't have to be that high.
Don't get me wrong. I think it's a good idea. It's usually cleaner than well-water too close to the latrines. My point is that it's not a no-brainer. There are potential problems that need to be planned for.
