I had a G2 outfit for a long time and it is the biggest regret of my camera ownership that I sold it. Now as they are getting older and older I think again about buying one, but am more nervous about it.
But LCD degradation, as others have said, isn't down to it being 'ON', but gettting old. I wouldn't normally take batteries out of a camera because for each time you do it the contacts and the battery can be contaminated with grease and sweat, eventually causing corrosion. Perhaps if the camera gets wet I would do it, but as the technical side of photography is largely about reducing the possibility of errors I'd be worried about running out the door with a fully electronic camera and no batteries in it! If you leave a gap for an error one will creep in.