Supremacy is a game-mode that revolves around you or a teammate getting into the exact space your opponent died in order to pick up something they dropped in order to build points and win the game. Since picking up the crests is the only way to earn points (with kills on their own having no bearing on the scoreboard), the more time between the kill and picking up the crest, the greater the risk of an opponent picking up the crest and denying your team those points. Thus, this mode promotes close quarters combat to minimise the kill-to-pickup time, meaning close quarters weapons are more effective in this mode. What is the most effective close quarters weapon? The shotgun.
TL;DR: If you hate shotguns, don't play supremacy.
If it became primaries only for a week, all you would see would be clever dragon and maybe last word and some doctrines (or equivalent). And you can't have missed all the posts about clever dragon being 'op'.