Good Morning Yoseikan Student:
Ever see how much dirt, gunk and germs that are brought in onto the floor by shoes (on a hardwood floor)? A better reason than most for bare feet... Also bare footed you can get a close look at ankle positioning and toe positioning... in shoes, you cannot see that and could build anatomically bad habits in your technique. Hense shoes off...
Gis are shapeless unisex clothing which equalizes everybody. Old, young, executive or vagrent in a gi everybody is "neutral" and ther is no distinction.
Belts, that is simply a visual aid for a teacher to tell instantly what skills are available to build the lesson plan around. Without them and its much harder to do so, and especially for rotating instructors, or assistants assisting. Its a visual aid.
Stance training helps examine and explore the correct body mechanics of a technique. Random or haphazard and you'd be getting different results from the folks on either side of you. All starting from the IDENTICAL place (same stance mechanics) and you explore how power can be maximally generated from a seemingly "bad" position.
Flat footed or heel up, depends on what you are doing and attempting. Flat footed is my standard, but not "dead weight".
Karate done correctly is not bad for the joints. Only done INCORRECTLY is it bad...
And finally yup, the many arts of -te ARE about personal control. Command over your physical actions and exploring how to control the thought processes which trigger them. Figure out how to control either so that you cannot be forced into a situation, and you've learnt well...
Learn to control ourselves, so we AVOID the stupid and avoidable situations and we've learned correctly & well... IMHO-fwiw