I think it would be a lot better looking if when your weapons aren't Drawn (even for NPCs) you would put your shield on your back
Well, if you're looking for that kind of realism, so too should be displayed on a person: 2 iron maces, 7 hide armor, 2 ebony war axes, 3 iron shields, steel armor, steel boots, steel gloves, 19 potions, 12 gem stones, 2 mammoth tusks, 7 light armor boots, and an Elven warhammer, and this is all in addition to what I have equipped.
Realism means I can't really carry 400 "weight" of gear around Skyrim without adverse consequences.