Aluminium is pretty light... and you could machine it in some pretty cool ways to help eliminate some weight (if the weight was even a problem).
I suspect a heavier core might actually feel better. The heavier core would add some weight towards the center of the cube. Any added weight in the core of the cube, would not change the rotational inertia of the layers. In other words, the cube would weigh more, but the turning of the layers would feel the same. To repeat it another way, the cube would not slow down due to the added weight.
The problem with heavy cubes, in my opinion, isn't the cubes overall weight (we can all lift them...). It's where the weight is. A heavy cube, currently, has the weight mostly in the hardware, edges and corners. This creates rotational inertia which makes it feel slow and hard to turn (all other things being equal... of course cubie design factors in too).
Eventually, by design or sheer luck, we'll get a heavy core with lighter edges and corners... and it'll blow everything out of the water. The low rotational inertia would allow the layers to fly by.
The problem with light cubes, in my opinion, is that you lose control of the cube because you just don't feel it enough. I haven't yet ordered my Alpha CC, but it would be a great cube to try the heavy core light pieces hypothesis out on.
I've always loved the quality of the plastic from Alpha... if only Dayan could get Alpha plastic... oh well, maybe someday!