I know several horses that do dressage barefoot and they are absolutely fine. Besides, shoes limit the natural movement and circulation of the hoof, sometimes even numbing them, thus some people like them, because then the hooves are less likely to become ouchy. Hence the idea that shoes "protect feet". Barefoot definitely calls for more attention and care, but it is worth it.
That said, I respect people who have chosen to shoe their horses and do not intend to start a barefoot vs shoed war here. :)
I have come a long way, to surrender my shadow to the shadow of my horse.