From my own experience raising fry, my water quality is far better in a planted vs. a bare tank. I can put the same number of fry in identical 10 gallon aquariums, one with live floating plants, the other with fake floating plants (to offer them a sense of security).
In two days, I need to do a 50% water change on the fake plant tank, while the real plant tank can go a week or more.
I can 'overstock' a planted tank with no problems. I don't keep non-planted tanks anymore, but I was never able to maintain the fish occupants in the numbers I have now, in a plant-free tank, without a tremendous amount of work (water changes to remove nitrates) on my part.
The key, I believe, on whether a plant is going to take in enough nitrogen waste (they take in ammonia first choice, then nitrite, then nitrate), is if the plant is actually in the right environment to thrive.
Many (but not all) newer fish hobbyists have inadaquate lighting to allow for fast growth (and more nitrogen uptake). A 15 watt bulb over a 29 gallon tank (what my 29 gallon tank came with when bought as a kit) would barely keep any plant alive. At 1/2 watt per gallon and a tall tank, light is hard pressed to get to the gravel to do any good.
It now has 2x55watts with an vastly improved reflector. I can keep medium and high light plants in there now (although I must inject CO2 and add fertilizers ~including EXTRA nitrogen~ to run both lights, or risk algae taking advantage of the extra light). I must trim the stem plants weekly, or 'top' them, removing the bottom half and replanting just the tops. Everytime I take a portion of the plant out, I'm removing nitrogen without having to do a water change. The cut plant now goes into overdrive to repair itself and/or put out new roots, so takes in more nitrogen.
Another factor is the plants chosen for the aquarium. My own LFS do not sell many aquatic plants. A bamboo plant, or the dreaded 'mondo grass' is most commonly seen. Those plants cannot survive underwater long-term, let alone 'thrive.' As they decay, they add to the nitrogen waste of the tank environment.
Just my 2cents.
OC