What plant was 'original' to North America? Take a look in your garden and 99% of what is planted there came from overseas, Asia etc.
The concept of 'original' fauna and flora is very flawed. At what point in time does one say 'original' occured? Evolution is punctuated by emergance of new species and of subsequent changes in fauna and flora. I think the means by which US authorities, be they local or national, use to try and return an ecosystem to 'original' is usually useless, most often playing into the hands of herbicide suppliers, and has other side effects which are often even more negative.
Hygrophila polysperma is just one small item in a much larger issue. Vermont uses Sonar on lakes to try and rid them of Eurasian milfoil. Very good for the supplier and maker of Sonar herbicide - but useless in the lake and seemingly does cause side effects to fauna as far as I have observed. In this case, a weed cutter or some good old fashioned work might help to rid some inlets of this plant rather than using herbicide.
The issue is: who has the knowledge and right to say what is original in terms of species. Plants, seeds, pollen travel in the air, by water, by animal activity.
There are a lot more environmental priorities to address: rural runoff poluted with lawn chemicals; domestic use of chemicals which accrue in the environment, etc.