Why do floor tiles exist?
"Floor tiles can be beautiful and stylish, adding color and interesting patterns to a room."
I think you answered your own question.
Edit
Responding to your rephrased question.
Most floor tiles are very functional and can take a lot of abuse which is one reason they are used in commercial settings. Same in homes. In playrooms, kitchens, etc. that get a lot of hard use they will wear better than linoleum or carpeting.
I think in many applications it's functionality/durability over beauty. Again, they can also be very attractive but beauty is and always will be subjective and personal. Flooring is always a balance of durability, beauty and cost.