Chicken tree ornaments? ... Clover gave me one, and it will probably see action on the tree for a couple years, and then will become a [hobbit-word-for-useless-trinket] of some small legend, gracefully passed on.
Chickens on other stuff? Um, probably not.
I like chickens. They're personable birds, and they're great friends to have. I think the same of cats, and horses. Do I want cats on everything, or horses? No. It doesn't fit my decorating scheme, nor my idea of pretty. Photos of chickens, good paintings of chickens, yes, nice. Cute artist's conceptions of chickens? Um, no. I do not have, and will not have, wallpaper featuring chickens marching around the kitchen. (The kitchen is a really bad place for chickens anyway. It's unsafe for them, and unhealthy for us.) Thus, I will have no need of matching kitchen towels, or napkin rings, or the most cunning salt-and-pepper shakers, in a chicken theme, just because they're chickens. Kitchen towels are always nice, but they might as well have been some other design, or even plain.
This also goes for geese, ducks, cats, squirrels, frogs, and almost any other creature. I like them, yes. But my taste runs more toward National Geographic-quality images of them than it does to stylized drawings and stuff that is not useful.
While objects that only have decorative use are nice for some people, I really have no use for the vast majority of them. If it has to sit on a shelf somewhere, just to be looked at, it's probably not the thing for me. Back home, I have an exquisite carved wooden red squirrel. One. That's all I have, want, or need. My taste in things that are purely decorative for sitting places, that can't be used or worn or made into something, are picky enough that I doubt I can write definitive rules for it in one sitting.
At least oven mitts with chickens on them are useful, and eventually wear out.