Algea-Can we win the battle?

Here's something about aquariums that I find very intriguing. Algae have been around on earth far longer than aquatic plants. They have a evolutionary head start . So how can a home aquarist win against algae? Are 100% algae free tanks impossible? Seems to me unless we physically remove every trace of algae from the tank (by sterlizling, boiling the water etc) they should exist in the tank and be just as happy as plants when it comes to uptaking nutrients. However, some types of algae may have evolved so that they harvest essentially macro nutrients from their inorganic compounds exclusively and other evolved to utilize organic compounds. So in a ecological system where spores of both forms exist, one would compete and replace the other depending on the available resources. But I dont understand how aquatic plants can outcompete algae for nutrients, it seems to me that algae have evolved far efficient processes, in fact the biomass of algae in waterbodies, I think, exceed that of plants.
I think grazing is the best defense against algae, in fact that is how algae populations are controlled in nature, stable water systems overrun with algae signal a change in the dynamics of the water body and an absense of predators. In such situations algae populations are limited by the algae themselves. Inherent competition among algae in a closed system like a aquarium cannot be negligible. Moreover, algae populations will grow to match the supply of nutrients, which is where uptake by plants come in. However, algae will survive and utilize nutrients in micro quantities, if they cant, they'll be replaced by those that have evolved to do so.
after this long rambling meaningless post, my question is what are your thoughts on how algae are limited in stable tanks? It seems almost impossible, given the diversity and tenacity of algae.