Sounds like an experiment I did once a long time ago. Back in those days water hyacinth not doing well was a huge mystery and of course nutrients were suspected, along with water temp, air temp, and a bunch of other things. People reported either their water hyacinth did great or they just didn't grow. Always the same symptoms, including a small root system that was basically black while healthy plants are huge (2-3' long) root systems with white and purple healthy looking roots.
One of the missing nutrients people thought could be the cause was potassium. I had the same concern as you...I didn't want to dump a bunch of potash into the pond if that wasn't the problem. If it was the problem I wanted to test the effect on fish.
So I set up 2 plastic garbage cans, filled with pond water and placed a single sick water hyacinth plant in each. In one I added 5 lbs of potash. That's a ridiculousness amount of course, but it was an experiment.
Two interesting things happened. First both plants took off growing. Big leaves, multiplying. Told me adding potassium was not needed. Also showed me what a low level of nutrients plants need to grow. These were closed systems. I only topped off to replace evaporated water (this was in San Jose CA).
The second thing it showed me was potash seemed to have no effect on fish. Unknown to me the plants had goldfish eggs on them, which hatched and the fry developed normally in both test tanks.
Have some other experiments I determined that the poor water hyacinth growth was due to goldfish eating the roots. The constant trimming just never allowed the plants to be healthy and just barely stay alive. Why fish in some ponds ate the water hyacinth roots and fish in other ponds didn't was unknown. I suspect that water hyacinth root aren't that tasty and so if a pond has other food available, like a tasty algae, the fish go for that instead.
No one ever reported seeing fish actually eating the roots. But every time someone moved sick water hyacinth to a separate tank, or into a filter, they took off growing.
I suggest a similar experiment.