Well, plants need CO2, light and nutritients, and o2 at night. How they get that is not relevant. But of course some of them would grow better with their roots planted into some sort of medium which isn't too big to prevent the roots from spreading.
In terms of nitrAtes many species don't care about the level. What matters is that before it becomes nitrAte it's been in the form of organics first(bad in itself), then toxic ammonia then nitrIte, then finally nitrAte. All these processes need lots and lots of oxygen as well which affects the enviroment. So having high nitrAtes is not a problem in itself, but the question is why. And that's presuming your nitrAte test is accurate which often isn't.
The best way to deal with that is to either target the organics via siphoning the substrate/cleaning the filters, feeding less, reduce stock, do more water changes, etc..or..A possible chemical approach is purchasing Seachem purigen which removes organics from the water directly preventing them from becoming anything else than that.
However, as already mentioned by other members, having lots and lots of plants that can utilize that ammonia before it starts converting to other forms is the most pleasing way and the fish would prefer such an enviroment. But it's not cheap or easy to have healthy and fast growing plants with little effort.
An alternative to aquatic plants would be emersed plants as they can draw CO2 directly from air and thus as ammonia/nitrite/nitrate removers are even more efficient than aquatic plants. I have some peace lilies, calatheas, etc..growing with their roots only in water planted in hydroton pebbles in planters like in the picture below. This may require modification of the hood or converting to open top aquarium but once done and the plants adapt, they start really appreciating the waste fish produce
and there's no need to worry about CO2 ever.
Here are some of mine: