Vectors with different orientation but the same magnitude are the same vector (the zero vector.) Observe that if you add a zero magnitude vector and a unit vector, the result is just the same unit vector. It follows that the normalization scheme you described can't be a function on vectors (since you can "normalize" two equal vectors but get two different results.)

> A vector with orientation but a magnitude of 0 is a completely valid vector afaik

Not by the mathematicians' definition. Maybe somewhere in physics such objects are useful, but if you formalized them you'd get something other than a vector space.