Moisture is the problem from winter, concrete will draw moisture and cause rusting. The carpet/ plywood method is a moisture barrier not to stop flat spotting tires.
Ah, you like to play on words, uh?...........I ask you, "What is softer?" Oh yeah, rubber. I use a lift to store my bikes. I let the suspension sag just a bit and let the tires lightly touch the wood.
Why is it that when tires sit on cement for extended periods that they leave a stain(imprint) behind?