For people unaccustomed to going barefoot in public, practicing a traditional Japanese martial art can be surprising or uncomfortable. Other than just because that's how it's always been done, there are several practical, functional reasons for practicing martial arts barefoot.
- It provides a good, uniform ground interface. If we cut out the variables associated with shoes, uneven surfaces, etc... we can concentrate on other variables in our training. (Of course, eventually you are going to want to practice this stuff with shoes on uneven surfaces of different textures with varying lighting conditions, etc... But in the dojo it's shoes-off.)
- There are supposedly health benefits to going barefoot. For an interesting look at some of this info, check out this article.
- It helps to keep the mat surface or the dojo floor cleaner. Nobody likes wallowing in the filth tracked in on the bottoms of people's shoes, so the shoes are left at the door or the edge of the workout surface. It is thoughtful to bring a pair of flipflops or slippers to wear whenever you are off the mat to keep your feet clean.
- Shoes can tear the surface of the mats or break down their resiliency, forcing us to replace them more frequently at great expense.
Besides... It's just that's the way it's always been done.