This is a fascinating thread. I have always known that plants would eat the nitrates but didn't know they would work directly on the ammonia.... and I am still not totally sure that is what you are all saying.
Has anyone done any work on its effectiveness with different water types, hard and alkaline against soft and acid ?
They don't, the bio-media in the system does. The plants work as a filter removing nitrates. Imagine it as if it were a regular trickle filter; first you have waste from feeding, poop, etc., that gets introduced to the tank. A trickle filter first catches the solids with a mat or sock or some other mechanical filter. The water then continues on down through the biomedia, generally this is kept as a wet/dry area but doesn't have to be as all surfaces in the system can grow bacteria. These bacteria break down the ammonia and nitrites into nitrates. These nitrates stay in your system unless removed with a denitrator, water change, or plants. This is the reason why plants should be more popular in the hobby.
Imagine setting up a place to grow your own food in you house that is both beautiful and makes your fish keeping experience more enjoyable! There are limitless applications and designs. I know of people using their normal house plants as the filters with multiple lines secretly running to each of them. Some people are growing TREES.. not lying, they are. I'd like to grow beautiful flowers and some of my favorite veggies. I can do all of this and raise happier healthier fish and change my maintenance from water changes and filter washing/replacing to picking flowers and harvesting crops and occasionally topping the water off.