My dh is an aquatic toxicologist, an environmental scientist who specializes in water quality and water toxins. When we had a pond, with a stream to keep the water flowing and aquatic plants, we still had to put some stuff in it to kill the algae. Algae bloom can be toxic to humans. My point - there is no such thing as a completely natural pool or man-made pond because real ponds and pools have water circulating in and out of them - streams and rivers. Our pond had circulating water but it was still the same water. Any water that just sits is going to be susceptible to all sorts of potentially hazardous toxins. Now, that does not mean that chlorine is the answer. I do worry about chlorinated pools when we go swimming. I grew up with a chlorinated pool but my dad did not use as much as a rec center pool does. We just don't go often and only stay in a max of 45 minutes to avoid overexposure. If you have your own backyard pool, looking into the alternatives to chlorine is a great idea. But, you still need to have something in the pool that is going to prevent your family from being exposed to fecal matter, bacteria, viruses, not to mention the hazards that come from the occasional animal or bird that strays into the pool by accident and drowns.
nothing filters better than aquatic plants 
And the kids don't mind - they love the lake.
