It is possible to roll your ankle bare foot or in shoes. However, on a smooth surface like a tennis court, I think it is easier to roll your ankle wearing shoes as they lift your foot off the surface and tend to fail critically and roll or trip you.
However, most tennis players want shoes because they do protect the foot from abrasion and impact.
I'm not a fan of the super-heavy, combat boot style of tennis shoe and prefer a more minimalist design. One of my dislikes is that so many shoes have a raised heel. This is actually an unathletic position because it pre-tenses the calve muscles and limits the ability to push off. Just as sprint spikes do not have a built up heel, the footbed of a tennis shoe should be level in my opinion. I'm interested in trying the new lightweight shoe from NB. I'd like to see a tennis shoe that weights under 10 ounces but still has a decent outsole.