Well, with 30 seconds of Googling, I found this:
Link here: https://www.peabodymemphis.com/peabody-ducks
"Raised by a local farmer and a friend of the hotel, each team of Peabody Ducks lives at the hotel for only three months before retiring from their duty and returning to the farm, where they are free to live as wild ducks. With a return to the great outdoors in mind, the hotel recognizes its resident waterfowl as wild animals and does not domesticate them or treat them like pets."
It's truly amazing what you find when you just take a moment to do just a little itty bit of research. 🙂
I think they're just fine. And your observation of "When the ducks arrive into the fountain, some of them immediately feel the need to rush to a podium to grab it quickly before another duck did" is quite possibly your own projection onto the situation. That may not be - and probably isn't - what is occurring.
It's a cute tradition. It's not harming anyone, or any creature.