If nutrient load and bright lights caused algae then the Estimate Index 'high tech' approach to the hobby would not work.
Interesting - eutrophication in natural but polluted waters is generally linked to levels of Phosphate, at quite low levels, and Nitrate at higher levels than Phosphate, but still quite low compared to those in most aquariums. EI is indeed quite generous, 1-3 ppm for Phosphate, 10-30 ppm for Nitrate. I'm not a scientist so I don't express an opinion just a concern about apparently conflicting views.
Observation. Algae in my ponds is not problematic when water temperatures are low, the days short and the light intensity low. Unpicking the three is not easy. However, especially in the late spring, before the higher plants have dominated the ponds, algae can be very much the dominant photosynthesis based life form. One pond is shallow, a wildlife pond, one is deeper and has goldfish. The latter will have green water in spring which I solve with UV and filtration, very effectively. My ponds have only trace levels of Nitrate and Phosphate and the water is also generally quite soft, below 60 TDS in the wildlife pond and below 100 in the goldfish pond.
I aim to keep the water column in my planted tanks at levels of Nitrate <10 ppm and Phosphate <1 ppm. It does not stop my plants getting algae on old leaves, or sometimes on the roots of floating plants, and green filament algae seems in my experience to grow pretty much in the same environmental conditions as higher plants but if I let levels of these two nutrients consistently fall below levels which I can measure, I seem to suffer from poor plant growth, which is I suppose no surprise. My experience is that Phosphate levels above 5 ppm are associated with severe algae problems, but it may not be a cause and effect. Above 50 ppm of Nitrate algae problems all seem to be an issue. Higher temperatures and higher light levels seem to encourage light green string filament algae. Darker clump forming cladophora seems to like less intense light and accumulated organic material.
Used to treat acne or have I got muddled? I thought there was evidence it is, as a low level water pollutant, beneficial to algae growth? I have never knowingly used it as an algaecide. I have found electrolysis virtually useless. Hydrogen peroxide works to a point. Though generally I go with nature and reduce light intensity, cut back on light duration or let the floating plants take over more of the surface. I've always found a photo period of full lighting more than 10 hours problematic for algae and sunlight hitting a tank is also problematic. I've also found low CO2 levels seem to damage plants and then algae takes advantage.
Strongly growing plants stop algae not by reducing nutrients but by releasing chemicals that are algaecides
Allelopathy is real, I know that, in the water kingdom I first heard of from Dianna Walstad, some I have read are less convinced of its importance in the matter of algae, and suggestm that in flowing waters this chemical process would be very difficult, in stagnant pools, matters may be very different.
I would be delighted if you and others might have some views and reading to recommend. But I stress I am not a scientist and I genuinely find chemistry in the hobby a challenge, not false modesty, just the truth.