Two notes on that:
1) If you are growing plants hydroponically (only roots in water) then they are releasing O2 into the air, not the water, so you will still need mechanical oxygenation.
2) Most plants prefer ammonia to nitrites or nitrates, so you may as well skip the bacterial filter and use plants for the whole process.
Plant filters are very effective, the only real drawbacks are the space they take up and the lighting requirements.