Given the incredible number of chickens that are processed every single minute across the world, this shouldn't be surprising but it's easy to see why you might be surprised if you never considered where all the stuff that isn't meat goes.
It’s also because real feathers are similarly durable as plastic feathers would be. Plants are very cheap to grow as well, but plastic plants are nevertheless a thing.
Feather meal is used in animal feed.
https://en.wikipedia.org/wiki/Feather_meal
Manure is also fed to cows.
https://extension.missouri.edu/publications/g2077
"Poultry litter can be used as a feedstuff... There are currently no federal or Missouri regulations governing the use of poultry litter as a feedstuff"
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I found it pretty surprising. It would not have surprised me at all if we made fake plastic feathers and burned or buried even more real ones because it works out fractionally 'cheaper' to make new then collect and wash/treat the old.