There is some misunderstanding in this thread, so I will try to clarify things.
First, algae has nothing to do with nitrates. algae is natural in any healthy aquarium with fish. Keeping it in check so it does not become what I term "problem algae" is a matter of the light/nutrient balance. Nitrates may be high due to excess organics which can certainly be one factor in the balance, but high nitrate in and of itself does not mean algae problems. Problem algae can be present in tanks with zero nitrates or in tanks with higher nitrates; they are two distinct issues.
Plants do not use nitrate as such. Plants obviously require nitrogen as one macro-nutrient, but unlike terrestrial plants (which prefer nitrate) most aquatic plants prefer ammonium as their nitrogen source. Scientifically-controlled studies have shown that most aquatic plants will take up all available ammonium/ammonia and only then turn to nitrate when the ammonium is no longer sufficient and provided it is still needed (in balance with the light and other nutrients). [There are studies suggesting nitrite is the plants' second preference, even before nitrate.] This is because the ammonium can be immediateely used by the plant; nitrite and nitrate must first be changed back into ammonium by the plant before it can be used, and plants do not waste energy when it is not necessary.
The reason nitrate is usually low in low-tech or natural planted tanks is not because plants take it up, it is because the plants are taking up ammonium/ammonia rapidly (faster than the nitrifying bacteria/archaea can) and this does not produce nitrite, so nitrate is less. Of course, high organics can cause high nitrates so the more fish the more organics and the higher nitrate may be, but it is common in low-tech/natural planted tanks to have nitrate in the 0 to 5 ppm range. My tanks have tested this for over a decade now.
Water changes are essentail in any healthy aquarium, and should be regular (once a week) and substantial (50-70% of the tank volume at one go). Nitrates should remain low with this, but nitrate is not the governing factor (unless it is high which is a sign of a serious problem biologically). All sorts of pollution accumulates from fish in an aquarium, and filters cannot remove this, nor can plants unless the fish/water ratio is extremely low and plants are significant. Water changes obviously will reduce nitrates if they are high, but the goal must be to get the nitrates low and stable, with never a rise in nitrate--a sure sign of problems with the biological system. Regular significant partial water changes will ensure a healthy balanced system, and part of this is that nitrates do not rise above the permanent stable level resulting from the fish load being in balance, the fish are not too large for the system, or being fed too much--all of which can increase nitrates and other contaminants requiring more water changes but also requiring a change in husbandry/management as any rise in nitrates from one water change to the next is a serious negative in the tank.
