I remembered seeing a University of Nebraska study years ago that mentioned examples, and one was of a cattail stand that was first cut in August of the previous year. Then the water level was raised, and kept high through the winter. Less than 20 percent grew back the following year.
So we started recommending that people mow frequently enough to prevent the plants from emerging again. We have since bought back several of our customers' Lake MowersTM after a year or two when their cattails were gone and they had no more use for the cutters. They reported the trick to getting rid of the cattails was to keep the plants below the water surface for long enough that they drowned.