The key word here is "residual!" Picture this. The ozonator can only oxidize the "bad" elements that physically pass through it. It does that well. But once the water passes back out into the pool, it has nor offers no residual oxidizing effect. And in fact can get "re-infected" immediately, and wander around in your pool, infecting you, for who knows how long, before it and its pathogens and bacteria happen to stumble through the ozonator again. Think about it, how long do you think it would take for every cubic foot of water to find its way through that one little unit? The answer is, uh, pretty much forever. Even if by some miracle you could wait that out, and all your water passed through it, the rest of your water is being subjected to new pathogens every time someone gets into the pool! Or when a bird flies overhead. Or any number of other ways nasties are introduced into your water. Does that sound like it's going to do the job and keep your family safe?
So how can they in good conscious sell these things, and claim they work? Well, that's why you'll find thier instructions dictate that you also use some amount of chlorine! Because chlorine, no matter where you introduce it into your water, spreads itself around to virtually every nook and cranny, and lies in wait to kill any nasty that happens by. It happens everywhere, on the spot, in real time, and even all at once, and happens quite quickly, so all of your water is protected, everywhere, all of the time. So technically the ozonator is working to kill stuff, it does, but not enough, and not fast enough. It's really the chlorine doing the heavy lifting. Which is why, for a typical outdoor residential pool, we generally recommend you skip the ozonator, and just use chlorine, because you'll be using chlorine either way!
You're way better off putting that money towards the purchase of a salt water chlorine generator, which makes fresh chlorine for your pool every few minutes, and keeps every cubic foot of your water sanitized, 24/7.
Oh, and if it wasn't obvious, again because they offer no residual protection, the ozonator is only doing its job when it is powered on and when the pool pump is running. And while it's also true that a salt water chlorine generator only makes chlorine while the pump is running, that chlorine remains in your pool, protecting you, long after the pump has stopped, like for the remainder of the day and through the night, until you run it again the next day!
That's what I think I know about it, anyway...