Right,
If I am on a concrete or tile floor I'm wearing shoes, period!
Hardwood or carpet, definitely barefoot, Linoleum, depends on if it's over wood or over concrete...
Mats, it's difficult to find a mat that's kind to a trainee's feet, at all. Toes might even need to be taped, especially for any kind of sparring situation...
I have a friend who has trained in a building near the San francisco Bay for many years, he always brings two pairs of training shoes, in case it's sunny, meaning the floor is dry and smooth, or foggy, meaning the floor is damp, and so will be comparatively tacky...
For sunny days, he wears his low-topped raquetball shoes, then on foggy, humid days, he wears the
Jing Mo boots (with recycled tire-tread soles)!
Ok, whatever we wear on our feet, or not, whenever we want to "root", it certainly helps to grip the ground with our toes!
Best,
Michael