There's some resources stating that most plants go for ammonia as a nutrient (and if there's less ammonia, less of it is converted to nitrate in the end of the process) and only a few use nitrates directly.
I'll answer based upon what I've learned on this over the years, although I caution that I am not a biologist.
However, to answer some specifics, not all plants use each nitrogen form equally. This varies among terrestrial plants and among aquatic plants. Your confusion comes from not knowing exactly the chemical process.
Plants use nitrogen (in various forms) as a building block for plant tissue. Urine, urea, feces, ammonia, nitrites and nitrates all contain nitrogen which is why some of these are commonly the forms used to provide nutrition to plants. Afaik, most plants can use each of these, although not with equal efficiency.
I'm not aware of any plant that targets only one form, although certain plants might do so at different stages of development.
The nitrogen source for plants in a fish tank is directly or indirectly almost always the fish food which contains proteins. Fish eat the food, their digestive tracks convert the protein and expel a larghe amount of the nitrogen in the form of urine. Protein is thus the source of the nitrogen.
You won't be able to use up all the ammonia just through plants because plants don't process the ammonia the same way or as fast as bacteria. BB for example can double it's population every 8 - 24 hours, for days and days as needed provided temps, pH, food, other nutrients, and proper surface areas are present.
While unicellular algae is able to double it's population in 30-70 hours, few hobbyists want algae blooms in their tanks. And algae is an example of a plant that wants ammonia as a spore, but nitrates as a plant.
http://aquarium-fertilizer.com/nitrate-no3-and-phosphate-po4-dont-cause-algae-ammonia-does
Large multi cellular plants (pothos for example) won't double in size every 8-24 hours.
In that condition, BB will grow to take over a large part of the nitrification process. Plants will still consume the ammonia they can find, but it won't be 100%. You could of course periodically eradicate the BB, but in that case, the fish would swim in water loaded with ammonia until the plants consumed it. Then the BB would start to re-flourish, etc.
This is in fact proven in nature. Plants have not exterminated BB in soil, lakes, ponds, rivers, or oceans, precisely because plants can't out compete the bacteria for these nitrogen sources. Bacterial populations explode when there is abundance, then dwindle and go into a type of hibernation when there is little to be found.
Perhaps some one will demonstrate that algae scrubbers can act in the manner you described, but I haven't seen anyone claim they are a better choice for filtration then the ones people normally employ.
