I have never seen or heard of anyone putting a stereo receiver in any sort of case, so using the Axe only at home, on your desk or wherever seems very similar to me, so unless you ever plan on taking it anywhere, I wouldn't bother.
Yeah, it'll get dust on it, but so would the rack case. Just dust it off once in a while. And when it's on, the fan will most likely move dust through the unit, regardless of whether it's in a rack or not, so I don't really see the benefit.
That being said, if you get a power conditioner or something like what Bruce has, then having it and the Axe, (and your amp if that's also what you use), in a rack is almost a given. Going back to my stereo analogy, when I had a full component stereo, with a tape deck, receiver, turntable, and CD changer, it was all housed in a nice furniture-style case.