I'll claim nurture, not nature. Dad was a semi-pro photographer with a keen eye. I grew up looking at good compositions. So did my sisters, whom became both graphic artists, one professionally. Our eyes were trained, not born. And I studied photography and arts for a long time, formally and otherwise. I can see compositions around me, but I can't invent them. I don't have the artist's or art-director's eye. I can move for better compositions, and I can get pretty creative in PP, but I just don't create imagery with the camera. I know and accept this.
So seeing compositions is easy; achieving them can be a bit of work; and the PP is definitely real work, and creative. For my first decade of digital photography, almost everything I shot was just raw material for the shooping machine -- grist for the mill, as it were. The K20D ruined that approach by forcing me to look more carefully, like back in my film days. I still like using P&S's because I can shoot more wildly, more freely, and shoop the hell out of what I captured.
So yes, it's work; and yes, it's fun; and I and others may have different opinions as to what works.
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EDIT/PS: I was going to mention that my other formerly shot portraits for money, with Bronica gear, and was very good with portraits -- and lousy with everything else, just couldn't 'see' compositions, still can't. I blame early training in music, not graphics.
IMHO visual composition is a learnable skill, much more than an inherent ability.
I'll also blame too much TV and cinema. With moving pictures, every frame is destroyed by what follows. One must study those ephemeral frames very closely to discern their setups. IMHO moving and still images require different compositional styles, often only tenuously related. To learn stills composition, study many many still images.