Randy, my only problem with your logic (if I understand it correctly) is that it leads to some pretty odd conclusions. If removal of ammonia can only be done by removing plants, then keeping plants is essentially keeping a reservoir of ammonia in your tank, ready to foul up at a moments notice. As such, having plants is, by itself, a liability.
With respect to inorganic nitrogenous waste, I'm more than content to call plant mass the successful removal of nitrogen from the system as it's essentially sequestered from interacting with (and therefore harming) much of anything.
If you follow the saltwater side, the effective removal of nitrogen from the system is accomplished by the trimming removal of the algae grown in the refugium/sump. Algae is far more of a liability than plants per say, because algae can die in mass quantities in a very short time. Some types of algae will die in mass quantities overnight as a result of reproducing.
The simple fact of the matter is that if you are keeping any living organism in your tank, you are keeping a reservoir of nitrogen in the tank. What happens to a tank when a fish dies, and is allowed to decompose in the tank? We see an ammonia spike. The same would be true if a large quantity of plants was allowed to die and decompose within the tank.
The best method for preventing this reservior from being an issue is to monitor your tank on a regular basis ~ as Billbug pointed out, most people don't allow a large dead plant mass to simply sit in the tank and decompose. But what happens when you are away on vacation or you simply get busy and don't pay enough attention to the tank?
While I agree with the observation that the plant mass has sequestered the nitrogen from interacting with (and therefore harming) much of anything, it has in fact not been removed from the system. The same amount of nitrogen is present in the system, although in a different form. As plants grow and you remove those plants to sell or trade, then you have effectively removed the nitrogen from the system.
On the saltwater side, aquarist regular harvest and trim their algae in order to remove nitrogen. Of course on the saltwater side, some also use deep sandbeds and most use LR and the anaerobic bacteria they contain to convert nitrates into harmless nitrogen gas and thereby gas off nitrogen.
Some of my hobby research over the past couple of years has been into the existence of similar anaerobic bacteria within the freshwater environment. If they can be used successfully on the saltwater side of things, they should also be able to be used on the freshwater ~ but that is a whole other discussion in and of itself.