I think it fair to say that many people who have practiced martial arts originally learnt indoors and in later years, on mats. If we're talking karate, then it will have been in Gi and barefoot. If your dojo leans towards self defence, it will have include thinks like knees and low kicks.
However, "real world", if you ever have to use your learnt skills, it won't be in a controlled environment, barefoot and on a flat surface. Students are obviously expected to practice on their own, and hopefully some of that would be outdoors and uneven surfaces with shoes on.
My personal favourite strike is with the knee, but that can be followed up by another one from natural instinct for me, a stomping kick, which I believe would be much more effective with shoes off rather than on. (Blame my Sensei and Naihanchi for these choices.)
The dojo in which I learnt includes outdoor lessons in normal clothing as a part of their training, as well as the more typical dojo lessons. Is this a common practice? Also, are there any specific aims in the teaching of lessons outdoors, other than those already suggested?
REY 26/02/2023