(Why) is using an uninitialized variable undefined behavior?

If I have:

unsigned int x;
x -= x;

it's clear that x should be zero after this expression, but everywhere I look, they say the behavior of this code is undefined, not merely the value of x (until before the subtraction).

Two questions:

• Is the behavior of this code indeed undefined?
  (E.g. Might the code crash [or worse] on a compliant system?)

• If so, why does C say that the behavior is undefined, when it is perfectly clear that x should be zero here?

  i.e. What is the advantage given by not defining the behavior here?

Clearly, the compiler could simply use whatever garbage value it deemed "handy" inside the variable, and it would work as intended... what's wrong with that approach?