I don't undered why you say "у кімнаті" but "на кухні"? why each one has a different preposition?
I think the rise of «на кухні» («на кухне») in Ukrainian (Russian) is connected to the fact that a kitchen is sort of an "area" in your apartment or house where you engage in cooking/eating activities.
There aren't any other rooms that use "на", I think (there is attic, though,— «горище» in Ukranian)
Room ís always a room and kitchen may be just a part of some other room. There can also be so-called summer kitchens, which are located somewhere outdoors
That's more idiomatic like English "on/in/at" (which don't correlate with Ukrainian). It's not that using "у" sounds awful, even native speakers can say something like "у кухні темно", "ремонт у (в) кухні", as I see.