Many rockered skis lack significant sidecut. Even for those that have it, it's not necessarily all that effective in the absence of a firm surface.
Further, consider that with a standard ski on a firm surface, the sidecut itself makes a major contribution to decambering when tipped and the ability to carve a turn that's smaller than the sidecut radius. Without decambering, you're stuck with the sidecut radius. With decambering, achieved when the ski is tipped and the skier balances against the turn forces, it is possible to carve a turn that is much smaller than the sidecut radius. And with more sidecut, more decambering will happen when the ski is tipped on firm snow. Make no mistake - decambering is a Biggus Dealus for a conventional ski.
So now consider the rockered or early rise ski. When tipped, its shape in 3D space (and powder is indeed a 3D medium) forms the necessary arc even without further decambering. You are correct that the shape of the turn is made (or at least strongly affected) by the shape of the ski. In powder, the rocker must be included as part of the shape that contributes to the turn. And, in powder, the decambering is not controlled by the sidecut against a firm surface, since the sidecut has no surface to work against. Instead, assuming the ski is not a 2x4, the ski bends because the skier places more pressure on the middle of the ski in a soft medium.
I have owned skis 110mm wide with essentially no sidecut. On firm snow, they were clumsy and required a great deal of active steering. In powder, they were wonderful and they turned when I tipped 'em.
So we're thinking that in powder, decambering (whether already decambered due to rocker or not) plays a greater role than sidecut? Thinking about it, I still feel that sidecut must play a factor, but that's just in my head, not really sure.
I know what you mean about tipping a fat ski in powder, it really does work (I have worked in Niseko for the last 2 seasons and ski Chopsticks).
On the pole front, I have lost a pole from not wearing the straps, I like wearing mine, manage to tomahawk a fair amount without stabbing myself as well.