For dealing with that floating FA around the perimeter, killing it is quick and easy however sending it as dead plant material to the bottom allows it to decompose and put ALL the incorporated or bound nutrients that grew the algae back into the pond basin - a recycling process None of the nutrients / elements that allowed the algae to grow were removed from the pond basin. The only thing added or net gain to the pond system was the chemical algaecide that killed the algae.

Best pond and beneficial management is to actually remove or harvest the algae. Harvest the crop that grew. A very useful tool for removing FA is a long handled smelt dipping net. This removal reduces the offending nutrients in the pond, the cause of algae, and lessens the amount of oxygen that was consumed in decomposing the dead algae. This helps keep the pond at a lower nutrient level. Removing the algae and associated nutrients reduces the total nutrient load in the pond helping to keep the pond at a lower nutrient level. Nature's way or process is to keep adding MORE nutrients to the pond basin to grow MORE plants that grow and die in the pond to eventually fill the pond with dead material until the pond once again is dry land - this is called aquatic succession. see more below

Another option to removing or reducing the algae is to get something to eat the algae and then remove the "critter" that ate the algae. A form of harvest. Then some of those nutrients that grew the algae are removed (HARVESTED) from the pond basin. Think of sheep or cows grazing on the pasture, then harvest the animals. Constantly removing a harvest crop from farmed land without adding nutrients back to the land will eventually grow less and less crop volume. Nutrients need to be added to harvested crop land to keep the soil productive. This concept also works in the aquatic system - a pond. Harvest or lack of harvest of things that grow in a pond affects the pond's productivity and ability to grow plants and animals. The more nutrients that enter a pond basin the more plants that will grow in that pond basin to eventually over time fill that basin with MORE nutrient / silt accumulation and dead organic materials - aquatic succession.

Pond Succession info
https://www.solitudelakemanagement.com/blog/the-stages-of-lake-and-pond-succession/

Start at 2:00 min in video