Nutrients and fertilizer.
It all depends on what you consider to be fertilizer. If you consider anything decaying to be fertilizer, then your pond is being fertilized continually.
Think of it as a large compost pile. Everything that falls into the pond is decomposed over time, and accumulates on the bottom.
The only way to remove nutrients is to remove them. That may sound funny, but it's true. Tilapia eat a lot of algae in a pond. When they die in the fall when the water cools down, many scavengers eat them, "removing" them from the pond. Raccoons, etc. Raking out the algae and weeds is another way to remove nutrients from the pond. BUT, they have to be put far enough away from the pond so that they don't decompose and leach back into the pond. Harvesting fish to eat is another way to remove nutrients. But, don't throw the fish carcass back into the pond - your goal in nutrient rich ponds is to remove nutrients, not add them back.
Phosphorous is a large part of the nutrient cycle, but for plants and algae to grow, they need nitrogen too. If there's enough nitrogen in the pond, and conditions are right, one pound of Phosphorous can grow up to 500 pounds of algae. Goose and duck poop are rich in nutrients. A single goose can poop one pound per day.
So, yes, you are on the right track of removing as many nutrients as possible, making sure that there is enough O2 at the pond bottom for bacteria to do it's thing, and reducing sunlight penetration into the water.
Some plants growing in a pond is a good thing - they use nutrients that would be feeding algae. Many plants are not - they reduce the useable area of the pond.
