Thanks to everyone who posted their thoughts. I love the discussions that are taking place. And it's nice to see that I'm not the only one who has considered the idea of "spheres".
Just to clarify, I define spheres according to critical interactions between Great Powers. A sphere, as I interpreted it, is just a group of powers that have immediate influences, quarrels, and/or contests over various provinces between them.
Based on this definition, it's easy to see why powers must control their sphere first before they can win. Bear in mind that the interactions between Great Powers in a sphere is only considered for the year 1901. I don't look beyond it because I believe that the first year is what defines the spheres as they are on the board. (Even England and Turkey can interact at some point, but this "point" is too far away to reasonably consider, so I only look at immediate interactions.)
I also don't consider the possibility of conflicts between inner powers—Germany, Austria-Hungary, and Italy—or powers that shouldn't fight early—England and Russia, Germany and Russia, etc.
Since powers must focus on their sphere before focusing on the other—this is the reason why interactions between powers in opposing spheres is ridiculous (at the start). For example, Germany and Austria-Hungary could fight in 1901, but think of how silly and counter-productive that would be. (Assume that the other Great Powers focus on controlling their sphere.) Since all powers are small at the start, it's silly to allocate resources towards conflicts that have very little gain, and which don't focus on important goals. It's more important for Germany to capture Denmark, Holand, and Beligum, and to resolve the West, than to fight Austria-Hungary.
And "controlling" a sphere means owning the majority of supply centers in it. The supply centers in a sphere are: all home supply centers of Great Powers in it, and neutral supply centers that are typically contested by those powers.
I've heard a lot of mention that Italy does belong to a sphere—but there isn't much agreement on what that sphere is. I've considered the possibility of Italy belonging to the Eastern Sphere—but I feel that this choice limits the flexibility of Italy's dynamic position. I think it's feasible for Italy fight a two-on-two battle in the Western Sphere with England or Germany as an ally against France. I know that this idea is fairly romantic and impractical, but the choice is there—and it's a choice that not too many powers have.