I said from my experience what worked. There's also many articles that stipulate the high Nitrate as having an impact on BGA along with other factors that influence its spread.
Every tank is unique in its own way. The details explain better and that is a problem on most forums. Even in my case, this algae might have been destroyed by something other than Nitrates. I don't see how putting antibiotics and nuking all of the bacterial flora helps. It' like punishing everyone because of a disgruntled individual.
Bottom line, having healthy plants will cause BGA to starve as there's little to no leak of organic matter into the water column. Cleaning the tank as best as possible of any decaying organic matter also helps in starving it.
Maintaining high Nitrates along with the above should make it go away.
Hitting it from multiple angles should do the trick, making the plants/beneficial bacteria suffer because of BGA will surely not improve the situation.