Story mode wouldn't play well using a traditional controller. To me it wouldn't make much sense at all if only 50% of the game was playable with the controller.
However, we will likely get native support for the steam controller in the future. (With a screen-relative control scheme... yay!) Also apparently you can plug up to 16 of them to the same PC. The local PvP could be insane
Yeah, no traditional controller support, sadly. It would be easier, especially for beginners. The inventory system could be easily (ok, it would be a lot of work) altered to support controllers, it's the animating a character to move in a way the works with controllers that would be difficult. At least as far as I understand.
Steam controller support will likely make an appearance, though. I don't know, but if What El Maco says about screen-relative control schemes is true, then maybe traditional controllers could see some support in the future. Pure speculation.