....Aside from a self defense situation, where it doesn't (shouldn't) matter, does anyone feel some sort of discomfort if practicing the arts without wearing at least part of uniform?
nope not in the least. Uniforms are but a reflection of the clothing worn by those in the country of origin of the art ( usually). I wear street cloths at least once a week when practicing and do not make my students wear a full uniform unless it is an important event or we know we are going to have guests.
Yes it looks better if someone walks in and everyone is in uniform but I just tell them we are having a casual "street' night. Hell I dont wear the uniform on the street so I need to practice in what i am going to be wearing once in a while.
When I attend class somewhere else I normally wear my bottoms and a tee shirt with no belt. however I will put on the whole uniform if I must