Yes, you are thinking about it correctly.
Organic "muck" usually accumulates under anaerobic conditions at the bottom of the pond. Under normal pond conditions, anaerobic bacteria are much less efficient at breaking down complex organic molecules.
If some silt washes in on top of this muck and isolates it from the water column, the net effect would probably actually be to remove nutrients from the pond. However, this is not beneficial for most ponds because losing depth every year can quickly turn a pond into a marsh.
For a pond that is well aerated, most of the complex organic material over an annual cycle can be broken down by aerobic bacteria. This turns the material back into CO2, water, and lower molecular weight organic molecules (such as humic substances).
As you have speculated, most of the nitrogen and phosphorus of these smaller organic molecules is now available in the water column as nutrients for the next batch of photosynthesizing organisms that are growing in the pond.
I think(?) your question is about removing at least a portion of this endless nutrient cycle from the pond?
There are several ways to do this:
1.) Physically raking the mats of filamentous algae out of the pond. They must then be discarded OUT of the watershed, so they don't decompose on the bank and the nutrients wash back into the pond.
2.) Tilapia eating a large portion of the organic matter. In warm climates (where the tilapia survive the winters) you eating the tilapia or discarding them as garden fertilizer does actually serve to remove nutrients from the pond. In cold climates you probably need to catch as many tilapia as you can at the end of the season, and scoop out as many dead ones as possible after the cold deaths occur. Unfortunately, many of the dead tilapia will not float to the surface.
I suppose to a lesser degree, crayfish eating some of the plants, then bass eating the crayfish, then you eating the bass would also remove some nutrients. Likewise with omnivorous minnows, or even catfish that do eat some plant material.
3.) Phosphorus binders have also shown some excellent potential in early testing. There are several threads on Pond Boss about these types of products. As more pond managers start using them, I expect we will learn the optimal way to use these products to reduce fertility in eutrophic ponds.
4.) I don't know how efficient this would be, but theoretically, if you deliberately grew shallow water rooted plants in your pond, and then drew down your water level and "harvested" the plants in the fall, then that would also serve to remove some nutrients. I do NOT recall any threads where people have actually done that, so I may just be making up speculative BS.
Finally, I think one of your best "bang for the buck" practices is to intercept as much as possible all of the NEW nutrients trying to make their way into your pond. Keep leaves, pine needles, etc. from ever entering the pond. If they do enter and are floating in some corner of the pond, then skim them out.
Surface water runoff into your pond will also start picking up some nutrients. Make sure your groundcover around the pond is lush enough to grab up those nutrients. If you mow the cover, never throw clippings into the pond.
I know I didn't provide any good and easy solutions. I think tilapia are probably the most efficient solution. (I believe you can stock them in Ohio.)
Good luck on your pond improvements!