Nitrogen (N), phosphorous (P) and carbon (C, mostly in the form of sugars) are all necessary for life. If any one of those elements are missing, life can not exist. Micronutrients such as potassium (K), calcium (Ca), magnesium (Mg), iron (Fe) and others are all necessary too but in much smaller quantities. None of those elements can substitute for one another, they are all used in different ways and they are all required. When water is deficient in nutrient sources, it is referred to as an “atrophic” condition - meaning it is missing nutrients. When water has too much of any nutrient in it, it is referred to as a “eutrophic” condition. Eutrophication of water leads to uncontrolled and unhealthy algae and bacterial blooms. Pool water is eutrophic but it is also aseptic because of the chlorine sanitizer in it. So while properly chlorinated pool water will not have significant algae or bacterial growth, it is always susceptible to biofouling (unrestricted growth) because of its high nutrient content. Reducing nutrient levels by either chemical removal (precipitation and filtration) or by water replacement will always help to reduce the incident rate and severity of biological growth. Phosphate removal is simply one strategy for making water atrophic.
As for SWGs, that is a more complicated issue. The concept of chloride electrolysis into chlorine is as old as the advent of modern chemistry and is the primary industrial method for producing chlorinating compounds. The processes used in industry are not quite the same as what’s used in a pool but the principle is identical. The problem is, in industry, their input water sources and chloride salts are all pure industrial grade chemicals. Water used in the process has no dissolved chemicals in it. So they never have to consider the effects of what the additions of contaminants can do to their processes. On the other hand, pool water is not only full of salt but also all sorts of contaminants like phosphates, nitrates and dissolved solids. All of these contaminants are susceptible to electrolysis and could, in theory, affect chlorine production. The problem is no one ever studies it because it’s simply not interesting enough to the manufacturer. So unless someone undertakes the time and money to look at the effects of dissolved contaminants on the chlorine production rates of an SWG, there’s nothing left but conjecture and hypothesis. There’s no motivation to study the issue because (A) no one dies from it, and (B) no manufacturer has problems selling thousands of these units per year. Perhaps some brilliant and motivated high school student will stumble upon this topic someday and win a 1st Place ribbon in their school science fair when they figure this out....