I would argue that it is not an efficient tool to fight or control algea growth simply from the fact that you cannot deplete them exclusively for algae and not for corals.Limiting food most certainly limits growth. It may not be the only tool, but to say that is not efficient (or does not work) is a stretch.
Quoting from the article heading this thread:"2. For major ions, the concentration does not vary by location or depth in the oceans. The only significant variation in major ion concentration comes as the salinity changes. Trace elements, however, are different, and can vary considerably by location and depth. Some are surface depleted. Some are depleted deeper down. No single number, for example, can tell you the natural ocean concentration of, say, iron. If one is targeting a “natural” concentration of iron, what number would one choose? The ocean does not tell us a definitive answer."Do they? Th ocean is fairly stable with regard to chemistry, as far as I know. I could be wrong (ignoring natural or unnatural sources in small localization, like volcanic activity, exposed ore beds, polluted outflow, etc.)
Although it is not an experiment as n=1 (my DT) and there is no control, I found that my Cheato started growing like crazy once I started adding TM trace A and K to my three-part dosing system. I have a lot of heavily fed fish, so N and P are not too high but never 0. My take is that the Cheato was growing much slower as one of the elements was rate-limiting. GHA followed by and is way too happy in my tank. So now I have decided to stop dosing the trace elements and see if I can reduce the GHA growth. Clearly, at some point, I will start dosing the trace elements, though at a much lower concentration. My sump contains GHA, cyanobacteria, Aiptesia, and countless critters, probably because I never dipped my corals (counting on my wrasses to do their thing). Time will tell if this strategy will work. Will update.