That's a good question. Being barefoot really goes back the the Eastern cultures where it is considered unclean (and just plain rude) to wear your shoes inside someone's home. It does keep the floor a lot cleaner. From a practical standpoint, it also helps when pivoting to not have a shoe gripping the floor. It is also harder to develop the proper kicking technique in shoes although the shoe offers some protection if the technique is not perfect.
However, noting that there is a difference wearing shoes, I have asked my sensei to have a "street clothes" night for self defense every now and again.