If it were just a thin copper sheet, you would have a hot spot directly behind the chip, with significantly less heat reaching the outer edges. A vapor chamber should allow the heat to get distributed more evenly. And it's not like vapor chambers and heat pipes contain much liquid anyway. It's mostly a vacuum inside them, with a residual amount of liquid vaporizing into a gas and recondensing to carry the heat elsewhere.
I suspect these things would be fragile, considering how thin they are. Perhaps they could be permanently adheared to the back side of a device's shell to increase their rigidity though.