Consider phosphates to be wood and algae to be flame.
Remove all the wood and you won't have fire. Or, keep the flame away and it doesn't matter how much wood there is piled up. Chlorine keeps the flame out, and it also oxidizes things like dead skin cells and suntan lotion, and it kills bacteria and viruses, too.
You'll have to keep chlorine in the water anyway, to keep it healthy, so why worry about the phosphates? I've never even had mine tested.