I could be wrong, heck, wouldn't be the first time, but my best guess is that those Magic Eraser will produce tiny little bits of material that could fill in the dips on the stone and make it work worse. Does that make sense? Like I said, could be wrong, but that's what I would think might happen. Better to follow manufacturer's directions (most, anyway) and use detergent and a stiff bristled brush. Doesn't take a hard scrubbing either, just lightly, and let the gentle action and the lather remove the worn off grit.
That's the treatment both my stones get and they're old, and fine.