There are definitely some cons to it, for sure! On looking into it's use in ponds more closely, it does seem to need some management. Putting in something to break water surface tension (a fountain pump or something similar) would help with preventing the duckweed from fully overrunning it, or you can rely on routine manual removal of the plant.
I saw a guy on YouTube (I'll see if I can find his channel to link him) using duckweed to feed his pigs. He had some kind of a strainer on a stick (looks like what people clean pools with) that he strained the duckweed out with, tossed it in a bucket and fed it to the pigs. I suppose I was picturing something like that! But admittedly, it is work to maintain.
If you live in an area warm enough, tilapia might be an option to help keep it under control, and make a nice meal for you at the end of it. Otherwise, larger goldfish will do the job and look pretty to boot. (Shubunkins would be better than koi--just as pretty, but only get to 24inches, and a lot cheaper!)
If duckweed isn't a great idea for you, some other fast growing plants that should help suck up some nitrates to fight the algae would include water lilies/lotus (gorgeous plants, though they will require a bit of maintenance between seasons), hornwort, parrot's feather*, and water lettuce. Most of those would contribute to your oxygen levels as well.
*I have parrot's feather in my fish tanks and LOVE it, but it can be invasive in some places so check the laws in your area before buying it.
It definitely should be a considered decision!! Best of luck in your bid for algae control.