You lift your tires off the floor so they don't touch the dirty ground. /s
Yeah you don't have to, just take the time to move the tires every once in a while to prevent flat spots. In all honesty, leaving it resting on the floor will only make your tires plastically deform (or at least slowly recovering elastic deformation) if they're really sitting for a LONG time. Putting some cardboard underneath the tires or anything that the tire will imprint into will help prevent flat spots.
Why are flat spots undesirable? Riding on tires with flat spots have noticeable bumps, that's it. You could probably make some arguments for uneven tire wear or safety issues, but really, its no problem.