The Bloch Sphere

First a little bit of background: A qubit is the analog of the traditional bit. Bits can be either 0 or 1, whereas qubits can be 1, 0, or both 1 and 0 at the same time. Because of this ability, it follows nicely that any string of n qubits can represent all numbers from 0 to 2ⁿ-1 simultaneously. So for example, 3 bits in a regular old computer can only possibly store one of the following values at a time:

000
001
010
011
100
101
110
111

These represent the numbers 0 through 7, a total of 8, or 2³, numbers. 3 qubits, on the other hand, are capable of storing all 8 of those numbers at once. That, essentially is the power of qubits. They allow for a quantum computer to perform operations on many values at once. As it happens, qubits are often represented visually by a Bloch Sphere. That's this guy:

A qubit's "state" can be anything on the surface of the Bloch Sphere, with the pure states of 1 and 0 being the polar north and south of the sphere. This leads me to the first big question I have on my quantum computing journey:

Why is the Bloch Sphere an ideal representation of a qubit?

So far, I have yet to find a really thorough answer to this question. My thinking is this: if a qubit can be 1, or 0, or somewhere in between, couldn't a simple linear scale in terms of percentages also represent a qubit satisfactorily? For example:

It just hasn't clicked yet for me. A qubit's implementation is essentially a certain property of a subatomic particle, for instance, the polarization of a photon. Photon polarization is already represented using a sphere called a Poincare Sphere. But in that case, there are precisely 6 different polarization states, so a 3D model of some sort does make sense. But the actual implementation of a qubit would only be concerned with two of those states, say horizontal and vertical polarization. And that's where I get stuck. Why are we still using the sphere representation? Fortunately, this confusion hasn't impeded me from studying further in quantum compututation. But it does irk me. I want a good answer to this question, and when I find it, I intend to post it here.