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It is hard to find any good information about the simple salt/simple clean system anywhere on-line.
That system is what we call an Ionizer System. It introduces a metal, typically and in this case copper, in to the pool. Copper is a pretty effective algaecide, so it keeps the pool fairly clear. But, copper has some significant downsides. It can cause staining, especially of hair. Ever heard of someone getting green hair from swimming? They probably blamed it on the chlorine, but it was from copper in the water. On top of that copper provides no oxidation of bather waste and no sanitation of the water. So all the sweat, skin cells, fecal matter (oh yes, plenty of that gets introduced when you swim), sunscreen, and various virus and bacteria are just swimming around in the water. The best oxidizer/sanitizer for water is chlorine, and pools with proper levels of chlorine take care of all those things mentioned quite quickly as well as kills algae.
I absolutely
HATE copper in pool water. All it does is prevent algae, nothing else, yet it is sold as some miracle cure that lets you use less chlorine. People are easily sold on that because most chlorine pools are managed very poorly so their experience is less than stellar. It's like if someone had only ever eaten burnt-to-a-crisp steak and decided that steak tastes bad. Using chlorine in the correct amount, as we teach here, creates a swimming experience that is worlds ahead of anything else. It feels better and is safer than any 'alternative' system on the market, especially ionizers.
So there really isn't much else to the system. It adds copper and tells you to run a low to no chlorine level and then shock occasionally to try to kill all the stuff that has built up over the week. Knowing what I know about pool chemistry I would rip such a system out in a heartbeat. Which I did with the mineral system that was on my pool when I purchased my house. It used silver, which is far superior to copper, yet still far inferior to properly dosed chlorine.