Why aren't unassigned local variables automatically initialized?

It seems like there is no way to have unassigned local variables in your code or check for them, as the compiler spits out Use of unassigned local variable error.

Why is the compiler not using default(T) on these variables at compile time?

Even if it's harder to do for value types, references types could easily be initialized to null in this case, right?

Here is some test code:

public void Test ( )
{
    int x;
    string s;

    if ( x == 5 )
        Console.WriteLine ( 5 );

    if ( s != null )
        Console.WriteLine ( "s" );
}

which returns:

Use of unassigned local variable 'x'
Use of unassigned local variable 's'

UPDATE:

For people who claims this is not allowed for a good reason, why is it allowed on a class level?

public class C
{
    public int X;
    public string S;

    public void Print ( )
    {
        Console.WriteLine ( X );
        Console.WriteLine ( S );
    }
}

This code compiles perfectly fine.

Why is it fine to have on a class level but not on a method level?