Here's a quick summary, and I apologize for some of the technical jargon.
Many fish can have impacts on aquatic systems.
But, let's talk about carp.....
Carp sure can and do have negative impacts on wetlands used by waterfowl. For one, they do graze on some vegetation that otherwise would provide food or cover for invertebrates that are in turn used by ducks. More sinister, though, are their impact on suspending sediment, that in turn shades the water column and bottom of a wetland, thereby having major impacts on overall plant production, and consequently on invertebrate production.
In addition, since they can become so abundant they can compound nutrient inputs (especially phosphorus and nitrogen) in the water column, by defecating in the water and by stirring up sediment which contains a lot of nutrients itself, that further shades the water column by promoting growth of algae. Not that algae is all bad, but when a wetland is already in a turbid state the natural algae in the water, further fueled by high nutrient levels, can become extremely abundant since there are no invertebrates or zooplankton to keep it in check.
If nothing changes (e.g. winter kill, fish toxicant treatment, or a series of good dry summers), the wetland will remain in a stable turbid state, and the bottom line is less than perfect for waterfowl.
Some people can live without wild things......I cannot!!