I recommend the usage of excel or h2o2 to "eradicate" algae all the time. But if you do not have a proper balance afterwards, it is pointless as you'll just have to do it again.
The common "algaecides" available in stores usually kill plants too.
Too much light, too little co2, and too little ferts are the problem 99% of the time. If you keep them unbalanced, you'll fight a million battles and never win the war.
I think sometimes you need to "kill" the problem or you'll never eradicate it. For instance, my BBA is invincible. It takes very high glut concentrations to kill. H2o2 has done nothing. But if I get most of it and stay on top of it, I can prevent it from coming back. But if I get everything "right" it will not just go away on its own... ime.