Even though they can be cleaved relatively easily, they don't necessarily have the same malleability that a liquid compound has. To fill in the miniature gaps and crevasses in the die and the bottom of the heatsink, a certain amount of 'flow' has to be achieved. A solid metal, regardless of how soft it is, will only move around so much. If you were to come up with a metal with the consistency of Jell-O, that would probably work =p.
The other issue I see is thickness... Thermal pads and heatsink gels compress to a thickness that's thinner than paper. You'd have to start out with a sheet of metal so tiny that it wouldn't add too much pressure on top of the die when the heatsink is clipped on. And when you have a sheet of metal that small, it's likely going to be reducing the 'flow' of the malleable metals. Anything thicker and you'll probably break your die when you bolt on your heatsink... Either that, or you're heatsink won't be properly mounted and you are losing performance anyway.
