Any two consecutive piano keys make an interval of 1/2 step (e.g. C to C#, or E to F). Why not just rename that to be a whole step, and avoid having to use fractions? Then, for example, C to F would be 5 steps instead of 2.5, and an octave would be 12 steps.
Just wondering if there is a good reason why it is the way it is, other than, "That's the way it has always been." Would music theory be drastically different if intervals had been named this way all along?