Yes, you probably could just have the tile floor, without shavings on top. It would certainly make cleaning easier. However, there are a few advantages to shavings:
Odor control: Shavings and other bedding absorb moisture, which lessens the odor in a chicken coop. This makes it more pleasurable for both humans and chickens to spend their time in the coop. It also attracts fewer flies/other insects.
Cushioning: Bedding provides a softer landing for chickens when they jump down from a roost. Jumping onto a hard floor, be it concrete or tile, is probably a lot more stressful on a bird's body than landing on a soft pile of shavings. Hard floors can occasionally cause leg and joint problems with chickens, or may lead to inflammation of the foot and future bumblefoot.
Insulation: Chickens are pretty good about staying warm in the winter, However, if temperatures get frigid, they'll appreciate any insulation they can get. Bare tile floors have a tendency to get cold quickly, and won't insulate the hens from the cold ground very well. A layer of bedding helps at least a little when it comes to winterizing coops.
