That's the thing, though. The animals at a zoo are their assets. These animals are under their care and supervision and they had to pay to get these animals just the same as anyone else. They maintain the animals and care for them just the same as well.
Frankly the birds are often last on the list for a breeding program unless it is a rare or endangered species. Much of the captive breeding takes place ammong the larger and more exotic animals. There are many tigers born each year in zoos. They don't have time to worry themselves over breeding the wild waterfowl and other more common birds. Many of the birds are just there as fillers for more variety, but most zoos don't pride themselves on their collections of wild waterfowl.
The private sector and the zoos make their money in different ways. The private sector makes the money from their animals by breeding them and selling the offspring to others of the private sector. The Zoos make there money by charging others to come and look at the animals they have. They don't have to breed the animals they have in order to make the money they need to stay afloat.
Much of the breeding in zoos is for species conservation and even then they don't normally sell the animals, unlike those in the private sector. If you had a rare species which was under a conservation program, then perhaps they would work with you and establish a breeding program.
They don't have to breed the waterfowl they have and so they don't. It's as simple as that.
If you want to help them out go and volunteer your time. Get to know them better and offer the occasional helpful nudge. That's how you get started with things like that. You can't just walk up to them and ask out of nowhere if you can help with their breeding program.
If they don't have a breeding program they won't incubate the eggs or allow others to incubate those eggs, regardless of any offers they get. They do value volunteers and staff members to help and maybe that way you can persuade some eggs from them after you help them to establish a breeding program.
If you want some extra eggs you may have to just trade with other breeders in the private sector to get the new species and make those same offers with them. Getting extra babies and a new species isn't what matters to them as far waterfowl goes, they just think differently about their animals than the private sector and breeders do.