> The fridge will be placed on the complete opposite side of the room from the island with the stove in it.
This is actually proper kitchen design (the island being in the way would be a problem, though). It's called a "kitchen triangle" and the proper shape and size of it determines how efficient a kitchen is (the third vertex is the sink).
A properly sized and shaped kitchen triangle can help turn cooking into a very efficient experience. One too large, or with an island in the way, or not correctly shaped (or not even a triangle) can make it a horrible place to cook in.
I will grant, though, that in some cases the kitchen doesn't ever serve a practical purpose, but instead serves as an interior "conspicuous consumption" focal point. Easiest way to tell if this is the case is how well used the appliances are; if they look showroom shiny with nary a splatter, dent, scratch, etc on them - you are likely not looking at a working kitchen.
Finally - all of this is moot if the person cooking is skilled enough. My wife has cooked highly commented meals for hundreds of people out of a kitchen smaller than some McMansion's walk-in pantry, using a stove that only had "on" and "off" (where "on" was set at 500 degrees F), and a work surface smaller than her cutting board (this was a "commercial" kitchen at one of here former employers who had a strange sense of what was the best things to spend money on - maintenance was not one of them).