IMO, algae will take hold when something interrupts the healthy growth of aquarium plants. Provided you have a well planted aquarium, an imbalance of light, CO2, or nutrients has the potential to allow algae to bloom.
...which brings us back to proper ratios. If anything is limiting in plant growth requirements, algae are more likely to grab hold and use whatever is there that isn't being used by the plants due to lack of something else. In that respect, I don't think it can be narrowed down to lack or excess of any one specific thing - be it lights, CO2 or nutrients. It would seem mostly case specific.
Since I feed mainly frozen food, this is probably why I have experienced the phosphate-algae correlation. FWIW, a while back, I started soaking my frozen food in RO water for about an hour before feeding. The health of the fish doesn't seem to be compromised in the least, and the orthophosphate present in all food is very soluble in water. I figure it can't hurt anything other than the algae I haven't had to deal with in a while. I thaw the food, let it soak, and pour it through a brine shrimp net.
I've been able to condition wild Apistos for breeding since doing this, which would lead me to believe that pre-soaking isn't removing essential nutrients to any large degree.
I think it's more that phosphate is a component of many food preservatives. Even the seafood you buy fresh at the market is soaked in a phosphate-containing preservative solution. It's very soluble, so that's the main reason I believe you can prevent some of it from going into your tank.
If you feed food that is pre-enriched with a vitamin additive solution, soaking may remove that as well. One thing you could do is look for a vitamin supplement and soak your thawed and drained food in that for a bit. Of course, be sure it doesn't contain phosphate! Most nutrients are in the tissue of the food, so unless the tissue itself is really damaged, I don't think nutrition is compromised to any significant degree. If it is, my fish certainly aren't showing it - fresh or marine.
Not to beat the horse, but one thing worth remembering through all this is that like Art said, phosphate is a major plant nutrient. Absence is no better than overabundance (maybe worse). The bottom line is that if all nutrients are available and light and CO2 are adequate, plants will tend to outcompete the algae. If things get out of whack, having too much phosphate, IME, doesn't leave you much time to get things back in order. I'd take an excess of about any other nutrient over phosphate.