Plants do not take up much nitrate, at least not those in low-tech or natural method planted tanks. Most aquarium plant species prefer ammonium as their source of nitrogen, and they can usually assimilate most all of it provided the system is in balance. Nitrate is only taken up when ammonia/ammonium is insufficient (in balance with light and the other nutrients), and this is because the plants must use energy to change the nitrate back into ammonium. Plants don't waste energy like this unless absolutely essential. There is actually some evidence that after ammonium they would prefer nitrite before nitrate, but this aspect has not been well studied. But it is their uptake of ammonia/ammonium that is the benefit.
Floating plants take up ammonia/ammonium very rapidly, which is why they are often referred to as "ammonia sinks." This is because floating plants have the aerial advantage when it comes to CO2. Submersed plants take up CO2 via their leaves, but floating plants with leaves on the surface or sometimes above it are able to assimilate CO2 from the air. Air assimilation is about four times faster than submersed assimilation for plants, and as CO2 is one macro-nutrient that is taken up in such quantities that it becomes depleted usually before other nutrients, it is easy to understand why floating plants are such rapid growers. Being closer to the overhead light, they also have a faster rate of photosynthesis, since photosynthesis is driven by light intensity (and spectrum), so the plentiful CO2 fuels this.
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