Structure is extremely important wether you're writing pop songs or "feelings" songs. In fact, structure is extremely important wether you use it or not.
I say this for two reasons. For one, it's all well and good to say "I'm just expressing my feelings so I don't really need a hook", but how can you expect anyone to listen to those feelings if the're not expressed in some sort of orderly way? I think of the saying "why burn the books if nobody reads them", why express your feelings in a song if nobody's listening? I personally think that songs that have something important to say deserve a hook. Also, if you're like me and you write many of your songs just for yourself to sort out your feelings, having some sort of structure gives you something to look back on and reflect.
second, it's very much ok to have a loose structure, or perhaps no perceivable structure at all in a song but, in order for this to work you must really really understand the basic building blocks of song structure. You have to know the rules before you can break them. I'm sure Bon Iver has spent a lot of time with common song structures and therefore he can write songs that seem to be almost structureless and yet work, feel complete, and are catchy.